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Slant helices in Euclidean 4space E 4
, 901
"... We consider a unit speed curve α in Euclidean fourdimensional space E 4 and denote the Frenet frame by {T,N,B1,B2}. We say that α is a slant helix if its principal normal vector N makes a constant angle with a fixed direction U. In this work we give different characterizations of such curves in ter ..."
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We consider a unit speed curve α in Euclidean fourdimensional space E 4 and denote the Frenet frame by {T,N,B1,B2}. We say that α is a slant helix if its principal normal vector N makes a constant angle with a fixed direction U. In this work we give different characterizations of such curves
ON THE QUATERNIONIC GENERAL HELICES IN EUCLIDEAN 4SPACE
"... Abstract. In this paper, we give some characterizations for a quaternionic general helix by means of curvatures of a curve in a 4dimensional Euclidean space. 1. ..."
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Abstract. In this paper, we give some characterizations for a quaternionic general helix by means of curvatures of a curve in a 4dimensional Euclidean space. 1.
InvoluteEvolute Curve Couples in the Euclidean 4Space
 Int. J. Open Problems Compt. Math
"... In this work, for regular involuteevolute curve couples, it is proven that evolute’s Frenet apparatus can be formed by involute’s apparatus in four dimensional Euclidean space when involute curve has constant Frenet curvatures. By this way, another orthonormal frame of the same space is obtained vi ..."
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Cited by 2 (0 self)
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In this work, for regular involuteevolute curve couples, it is proven that evolute’s Frenet apparatus can be formed by involute’s apparatus in four dimensional Euclidean space when involute curve has constant Frenet curvatures. By this way, another orthonormal frame of the same space is obtained
Pages 563–569 Smooth Euclidean 4–spaces with few symmetries
"... We say that a topologically embedded 3–sphere in a smoothing of Euclidean 4–space is a barrier provided, roughly, no diffeomorphism of the 4–manifold moves the 3–sphere off itself. In this paper we construct infinitely many one parameter families of distinct smoothings of 4–space with barrier 3–sphe ..."
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We say that a topologically embedded 3–sphere in a smoothing of Euclidean 4–space is a barrier provided, roughly, no diffeomorphism of the 4–manifold moves the 3–sphere off itself. In this paper we construct infinitely many one parameter families of distinct smoothings of 4–space with barrier 3
Metrics on the Moduli Spaces of Instantons Over Euclidean 4Space
 Commun. Math. Phys
, 1991
"... . We prove that the natural hyperKahler metrics on the moduli space of charge k instantons over Euclidean fourspace and on the space of ADHM matrices coincide. We use this to deduce formulae relating expressions in the curvature of a connection to invariant polynomials in the ADHM matrices corresp ..."
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Cited by 21 (1 self)
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. We prove that the natural hyperKahler metrics on the moduli space of charge k instantons over Euclidean fourspace and on the space of ADHM matrices coincide. We use this to deduce formulae relating expressions in the curvature of a connection to invariant polynomials in the ADHM matrices
The S 1 t × S 1 svalued lightcone Gauss map of a Lorentzian surface in semiEuclidean 4space
, 2008
"... We define the notions of S 1 t × S 1 svalued lightcone Gauss maps, lightcone pedal surface and Lorentzian lightcone height function of Lorentzian surface in semiEuclidean 4space and established the relationships between singularities of these objects and geometric invariants of the surface as app ..."
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We define the notions of S 1 t × S 1 svalued lightcone Gauss maps, lightcone pedal surface and Lorentzian lightcone height function of Lorentzian surface in semiEuclidean 4space and established the relationships between singularities of these objects and geometric invariants of the surface
The selfduality equations on a Riemann surface
 Proc. Lond. Math. Soc., III. Ser
, 1987
"... In this paper we shall study a special class of solutions of the selfdual YangMills equations. The original selfduality equations which arose in mathematical physics were defined on Euclidean 4space. The physically relevant solutions were the ones with finite action—the socalled 'instanton ..."
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Cited by 524 (6 self)
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In this paper we shall study a special class of solutions of the selfdual YangMills equations. The original selfduality equations which arose in mathematical physics were defined on Euclidean 4space. The physically relevant solutions were the ones with finite action—the socalled &apos
Serret–Frenet Formulae for Null Quaternionic Curves in Semi Euclidean 4Space R41
"... In this study, we construct the Cartan frame of a null quaternionic curves in semi Euclidean spaces R41 for an arbitrary parameter. ..."
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In this study, we construct the Cartan frame of a null quaternionic curves in semi Euclidean spaces R41 for an arbitrary parameter.
Polynomial time approximation schemes for Euclidean TSP and other geometric problems
 In Proceedings of the 37th IEEE Symposium on Foundations of Computer Science (FOCS’96
, 1996
"... Abstract. We present a polynomial time approximation scheme for Euclidean TSP in fixed dimensions. For every fixed c � 1 and given any n nodes in � 2, a randomized version of the scheme finds a (1 � 1/c)approximation to the optimum traveling salesman tour in O(n(log n) O(c) ) time. When the nodes a ..."
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Cited by 399 (3 self)
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Abstract. We present a polynomial time approximation scheme for Euclidean TSP in fixed dimensions. For every fixed c � 1 and given any n nodes in � 2, a randomized version of the scheme finds a (1 � 1/c)approximation to the optimum traveling salesman tour in O(n(log n) O(c) ) time. When the nodes
Antide Sitter Space, Thermal Phase Transition, and Confinement in Gauge Theories
 Adv. Theor. Math. Phys
, 1998
"... The correspondence between supergravity (and string theory) on AdS space and boundary conformal field theory relates the thermodynamics of N = 4 super YangMills theory in four dimensions to the thermodynamics of Schwarzschild black holes in Antide Sitter space. In this description, quantum phenome ..."
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Cited by 1087 (4 self)
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The correspondence between supergravity (and string theory) on AdS space and boundary conformal field theory relates the thermodynamics of N = 4 super YangMills theory in four dimensions to the thermodynamics of Schwarzschild black holes in Antide Sitter space. In this description, quantum
Results 1  10
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268,558