K. Nomizu S. Kobayashi, Foundations of Differential Geometry, vol. 1-2, John Wiley and Sons, 1963. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
First 50 documents Next 50
Passive Feedforward Approach to Bilateral Teleoperated Manipulators - Li, Lee (2000) (Correct)
....power, and M L , as defined in (7) is the apparent inertia that appears to the environment of robot 2. The n n skew symmetric matrix C L (q L ; g q L ) C L (q L ; g q L ) gC L (q L ; q L ) specifies the unforced dynamics of the target locked system by formally defining a connection [9] of the target system. For example, the geodesics of the connection can be used to prescribe the preferred direction of travel for the target system. The requirement that C L (q L ; q L ) should be skew symmetric is to ensure that the target locked system is a passive system with respect to a ....
S. Kobayashi and K. Nomizu. Foundations of differential geometry, volume 1. Willey, 1996.
On Relative Invariants - Fels, Olver (1996) (Correct)
....group on a vector bundle, and the relative invariants then correspond to group invariant sections of the bundle; the aforementioned cases are all particular types of tensor bundle actions. Unlike the preceding geometric objects, invariant connections, also of great interest to geometers, [17], 28] are associated with a generalization of the underlying multiplier representation, which we name an inhomogeneous multiplier representation. We show how this generalization can be readily treated using the same general framework. An additional class of important applications arises in the ....
....that the transformation rules (7.3) can be compactly re expressed in terms of the associated connection form Omega = du Gamma ) Omega ; 7:4) as Omega = Omega 24 Here Phi ( Omega w) Phi ) Omega ( Phi ) w for a one form and w a vector field on E. See [17], 27] for details. If the manifold M admits a G invariant metric ds , then the associated Levi Civita connection is automatically G invariant, but this is not the only way that G invariant connections can arise. Indeed, it is easy to give examples in which the group G admits invariant ....
Kobayashi, S., and Nomizu, K., Foundations of Differential Geometry, vols. I, II, Interscience Publishers, New York, 1963.
Motion Control Algorithms for Simple Mechanical Systems.. - Martínez, al. (Correct)
....on Q and 2(Q) the set of smooth vector fields on Q. Throughout the paper, the manifold Q and the mathematical objects defined on it will be assumed analytic. Associated with the Riemannian metric 6 there is a natural ane connection, called the Levi Civita connection. An ajfine connection [1, 23] is defined as an assignment v: 2(0) x 2(0) 2(0) x,r) Vxr which is ] bilinear and satisfies VfxY fVxY and Vx(fY) fVxY X(f)Y, for any X, Y C 2(Q) f C(Q) This implies that VxY(q) only depends on X(q) and the value of Y along a curve which is tangent to X at q. Let c: t [a,b] c(t) ....
....system, or pose coordinates g in the Lie group G, and variables describing the internal shape of the system or shape coordinates r M. This exactly corresponds to the geometrical notion of a trivial principal fiber bundle, which we briefly describe next. For further details, we refer the reader to [1, 23]. Assume that a Lie group G acts freely and properly on Q, I, GxQ Q In this way, the quotient space Q G M has a manifold structure such that the projection r: 2 M is a surjective submersion. We say then that Q(M, G, r) is a principal bundle with bundle space (2, base space M, fiber space ....
Kobayashi, S. and K. Nomizu: 1963, Foundations of Differential Geometry. Interscience Publishers, New York.
A Bayesian Approach to Geometric Subspace Estimation - Srivastava (1999) (3 citations) (Correct)
....trace . This suggests a direct formulation of the problem in terms of , rank complex projection matrices. Denote the set of all such matrices by . is a compact, differentiable manifold of complex dimensions, called complex Grassmann manifold, with interesting geometric properties, as described in [23]. Each element of uniquely represents a subspace (of ) of complex dimensions . Remark 1: Alternatively, a subspace in can also be represented by a (nonunique) set of orthonormal basis vectors. There are pros and cons associated with both the representations. In this paper, we utilize the pros ....
....gradient vector for function at point . This gradient vector points to the direction of maximum decrease in the function value, among all tangential directions. In the case of a uniform prior [ constant] the gradient vector (call it ) is given by or (9) where is called the Lie bracket ( see [23] for details) is called the gradient (descent) process of on if it satisfies the ordinary differential equation (10) This equation states that the velocity vectors at all points along this curve are equal to the (negative) gradient vectors at those points. Let be an open neighborhood of and for ....
[Article contains additional citation context not shown here]
S. Kobayashi and K. Nomizu, Foundations of Differential Geometry. New York: Interscience, 1969, vol. 2.
Metrics of positive Ricci curvature on bundles - Igor Belegradek Guofang (Correct)
....S p Gamma1 ae N is given by II(A; B) hrAB; r i r for A; B 2 fi . Thus, II(Y i ; Y i ) Gamma h 0 i h i r , II(U i ; U i ) Gamma f 0 f while all the mixed terms II(Y i ; U j ) as well as the terms II(U i ; U j ) II(Y i ; Y j ) for i 6= j vanish. Now the Gauss equation [KN63, VII.4.1] gives the sectional curvature of N in terms of the sectional curvature of (E Theta S p Gamma1 ; s r ) as follows: K g (Y i ; U j ) K sr (Y i ; U j ) Gamma h 0 i f 0 h i f K g (Y i ; Y j ) K sr (Y i ; Y j ) Gamma h 0 i h 0 j h i h j K g (U i ; U j ) K sr (U i ; U ....
....Ric g (U i ; U j ) 0 for i 6= j ; 4) Ric g (U i ; Y j ) 0. Proof. 1) follows directly from r r r = 0 , r Y i r = h 0 i h i Y i , rU j r = f 0 f U j , Y i ; r ] h 0 i h i Y i , and [U j ; r ] f 0 f U j . 2) follows from (1) 3) 4) By the Gauss equation [KN63, VII.4.1] we have R g (A; C; C; B) R sr (A; C; C; B) for any A; B; C 2 fi , A 6= B . By part (1) R g (A; r ) r is proportional to A , so R g (A; r ; r ; B) 0 if A 6= B . Now Ric g (A; B) is the sum of R g (A; r ; r ; B) and all the terms R g (A; C; C; B) so we get Ric g (A; B) ....
S. Kobayashi and K. Nomizu, Foundations of differential geometry, New York: WileyInterscience, 1963.
About Cartan Geometrization of Non Holonomic Mechanics - Tavares (2001) (Correct)
....by X q ; Y q ; but we omit the subscrite q when there is no danger of confusion) An affine frame for A q Q consists on a point P 2 A q Q together with a linear frame fX a g a=1; Delta Delta Delta;n for T q Q. We denote such a frame by fP; X a g. Let A(Q) the affine frame bundle over Q (see [7], section III.3) which is a principal fiber bundle with group GA(n) acting on the right of A(Q) by: fP; X a g Delta (a = a a ) A = A a b ) fP a a X a ; X a A a b g If fP; X a g and fQ; Y a g are two frames for A q Q, then there is a unique g = a; A) a a ; A a b ) 2 GA(n) ....
.... Gamma1 (U) U Theta GA(n) ae A(Q) 10 Now let us consider a generalized affine connection on Q, i.e. a connection on A(Q) Let e the corresponding connection 1 form, which is a ga(n) IR n Phi gl(n) valued 1 form on A(Q) e = a Phi a b (3. 9) By the general theory (see [7]) we know that on Gamma1 (U) U Theta GA(n) e has the following expression: e = Phi = a Phi a b = Ad (y;Y) Gamma1 ( Phi ) y; Y) Gamma1 d(y; Y) GammaY Gamma1 y; Y Gamma1 ) Phi ) y; Y) GammaY Gamma1 y; Y Gamma1 ) dy; dY) Gamma Y ....
[Article contains additional citation context not shown here]
Kobayashi S. and Nomizu K., , "Foundations of Differential Geometry", vol. I. Interscience Publishers, John Wiley & Sons, 1963.
Connections and curvature in the Riemannian geometry of.. - Privault (2001) (Correct)
....= div M (r M u v Gamma r M v u) Let (X 1 ; X d ) denote a set of normal coordinates at x 2 M with u = P j=d j=1 u j X j , v = P i=d i=1 v i X i . We have at x 2 M : r M X j X i = 0, X i ; X j ] r M X i ; r M X j ] 0, i; j = 1; d, and from [16], p. 282, div M (r M u v) l=d X l=1 hr M X l r M u v; X l i TxM = h l=d X l=1 r M X l d X i;j=1 u j r M X j ( v i X i ) X l i TxM = d X i;l=1 (X l u i ) X i v l ) l=d X l=1 d X i;j=1 u j h(X l X j v i )X i ; X l i TxM = d X ....
S. Kobayashi and K. Nomizu. Foundations of differential geometry. Vol I. Interscience Publishers, a division of John Wiley & Sons, New York-London, 1963.
Algebraic Theory Of Characteristic Classes Of Bundles With.. - Esnault (1997) (Correct)
.... homomorphism w = Phiw n : Phi n S n (g(C ) G(C) Phi n H 2n DR (BG(C ) assigns a de Rham cohomology class of the classifying space BG(C ) to a G(C ) invariant polynomial on the dual g(C ) of the Lie algebra associated to the C valued points of an algebraic group G (see [20], Chapter XII) In the unpublished note [3] Beilinson and Kazhdan give an algebraic description of w as an iterated Atiyah extension (see [1] Let p : E X be a (simplicial) principal G bundle on the (simplicial) smooth algebraic variety X over a ring k of characteristic zero. The exact ....
Kobayashi, S.; Nomizu, K.: Foundations of Differential Geometry, vol.II, Interscience Publishers 1963.
Normal Frames and the Validity of the Equivalence Principle - Cases In Neighborhood (Correct)
....along a path (curve) or on some other submanifold of the space time. The present work deals with the first two of these meanings of locally in which cases the equivalence principle is considered. The existence of (local) bases or coordinates in which the components of linear connections [3, 4] vanish at a point [2, 4, 5, 6, 7, 8] along a curve [5, 8] or in a neighborhood [5, 7, 8] have been considered. But with very rare exceptions (see e.g. 2] in the literature only the torsion free case has been investigated. The present work, which is a revised version of [9] generalizes these ....
....or on some other submanifold of the space time. The present work deals with the first two of these meanings of locally in which cases the equivalence principle is considered. The existence of (local) bases or coordinates in which the components of linear connections [3, 4] vanish at a point [2, 4, 5, 6, 7, 8], along a curve [5, 8] or in a neighborhood [5, 7, 8] have been considered. But with very rare exceptions (see e.g. 2] in the literature only the torsion free case has been investigated. The present work, which is a revised version of [9] generalizes these problems to the case of arbitrary ....
[Article contains additional citation context not shown here]
Kobayashi, S. and Nomizu K. 1963. Foundations of Differential Geometry (Interscience Publishers, New York-London), vol. I.
Affine-Permutation Symmetry: Invariance And Shape Space - David Sepiashvili Jos (Correct)
No context found.
K. Nomizu S. Kobayashi, Foundations of Differential Geometry, vol. 1-2, John Wiley and Sons, 1963.
A Riemannian Framework for Tensor Computing - Pennec, Fillard, Ayache (2004) (Correct)
No context found.
Kobayashi, S. and Nomizu, K. (1969). Foundations of differential geometry, volume II of Interscience tracts in pure and applied mathematics. John Whiley & Sons.
A Riemannian Framework for Tensor Computing - Pennec, Fillard, Ayache (Correct)
No context found.
Kobayashi, S. and Nomizu, K. (1969). Foundations of differential geometry, volume II of Interscience tracts in pure and applied mathematics. John Whiley & Sons.
Connections and curvature in the Riemannian geometry of.. - Privault (1999) (Correct)
No context found.
S. Kobayashi and K. Nomizu. Foundations of differential geometry. Vol I. Interscience Publishers, a division of John Wiley & Sons, New York-London, 1963.
Chern Classes of Automorphic Vector Bundles - Goresky, Pardon (2002) (Correct)
No context found.
S. Kobayashi, K. Nomizu, Foundations of Differential Geometry I, II, John Wiley and Sons, N.Y., 1966
Solutions Of Partial Differential Equations Using Symmetry And.. - Barco (2000) (Correct)
No context found.
Kobayashi, S., and Nomizu, K., Foundations of differential geometry, 1, Wiley, New York, 1963.
Vision Theory in Spaces of Constant Curvature - Yi Ma Shankar (1998) (Correct)
No context found.
S. Kobayashi and K. Nomizu. Foundations of Differential Geometry, volume II. John Wiley & Sons, Inc., 1996.
Vision Theory in Spaces of Constant Curvature - Yi Ma Shankar (1998) (Correct)
No context found.
S. Kobayashi and K. Nomizu. Foundations of Differential Geometry, volume I. John Wiley & Sons, Inc., 1996.
Passive Velocity Field Control (PVFC): Part I - Geometry and.. - Li, Horowitz (2001) (Correct)
No context found.
S. Kobayashi and K. Nomizu, Foundations of Differential Geometry. New York: Wiley, 1996, vol. 1.
Classical solutions for Hele-Shaw models with surface tension - ESCHER, SIMONETT (1997) (2 citations) (Correct)
No context found.
S. KOBAYASHI & K. NOMIZU, Foundations of Differential Geometry I, Wiley, New York, 1963.
Generalized Cylinders in Semi-Riemannian and Spin Geometry - Bär, Gauduchon, Moroianu (2003) (Correct)
No context found.
S. Kobayashi and K. Nomizu, Foundations of differential geometry, Vol. 2, Interscience Publishers, John Wiley & Sons, New York, Chichester, Brisbane, Toronto, 1969.
Theory and Computational Methods for Dynamic.. - Buja, Cook, Asimov.. (1999) (3 citations) (Correct)
No context found.
Kobayashi, S., and Nomizu, K. (1969), Foundations of Differential Geometry, vol. II, New York: Springer. 67
About a Decomposition of the Space of Symmetric Tensors of .. - Gil-Medrano, Amilibia (1994) (Correct)
No context found.
S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, I, Interscience, New York, 1963.
A Strong Maximum Principle For Weak Solutions Of.. - Andersson, Galloway.. (1996) (1 citation) (Correct)
No context found.
S. Kobayashi and K. Nomizu, Foundations of differential geometry, vol. 2, John Wiley and Sons, 1969.
A Learning Theoretic Approach to Differential and Perceptual .. - Amir Assadi Hamid (Correct)
No context found.
Kobayashi, S. and Nomizu, K. Foundations of Differential Geometry. Interscience Publishers
A Symmetric Product for Vector Fields and its Geometric Meaning - Andrew Lew Is (Correct)
No context found.
Kobayashi, S., and Nomizu, K. [1963a] Foundations of Differential Geometry. Volume I.
First 50 documents Next 50
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC