Results 1  10
of
36,761
HAMILTONIAN STATIONARY TORI IN THE COMPLEX PROJECTIVE PLANE
, 2005
"... Hamiltonian stationary tori in the complex projective plane ..."
ALMOST COMPLEX RIGIDITY OF THE COMPLEX PROJECTIVE PLANE
, 2005
"... Abstract. An isomorphism of symplectically tame smooth pseudocomplex structures on the complex projective plane which is a homeomorphism and differentiable of full rank at two points is smooth. Contents ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Abstract. An isomorphism of symplectically tame smooth pseudocomplex structures on the complex projective plane which is a homeomorphism and differentiable of full rank at two points is smooth. Contents
Hamiltonian stationary tori in complex projective plane
, 310
"... We analyze here Hamiltonian stationary surfaces in the complex projective plane as (local) solutions to an integrable system, formulated as a zero curvature equation on a loop group. As an application, we show in details why such tori are finite type solutions, and eventually describe the simplest o ..."
Abstract

Cited by 12 (1 self)
 Add to MetaCart
We analyze here Hamiltonian stationary surfaces in the complex projective plane as (local) solutions to an integrable system, formulated as a zero curvature equation on a loop group. As an application, we show in details why such tori are finite type solutions, and eventually describe the simplest
Relatives of the Quotient of the Complex Projective Plane By the Complex Cojugation
"... It is proved, that the quotient space of the fourdimensional quaternionic projective space by the automorphism group of the quaternionic algebra becomes the 13dimensional sphere while quotioned the the quaternionic conjugation. This fact and its various generalisations are proved using the results ..."
Abstract
 Add to MetaCart
the results of the theory of the hyperbolic partial differential equations, providing also the proof of the theorem (which was, it seems, known to L.S.Pontriagin already in the thirties) claiming that the quotient of the complex projective plane by the complex conjugation is the 4sphere. 1 Introduction
SURVEYING POINTS IN THE COMPLEX PROJECTIVE PLANE
"... We classify SICPOVMs of rank one in CP2, or equivalently sets of nine equallyspaced points in CP2, without the assumption of group covariance. If two points are fixed, the remaining seven must lie on a pinched torus that a standard moment mapping projects to a circle in R3. We use this approach to ..."
Abstract
 Add to MetaCart
We classify SICPOVMs of rank one in CP2, or equivalently sets of nine equallyspaced points in CP2, without the assumption of group covariance. If two points are fixed, the remaining seven must lie on a pinched torus that a standard moment mapping projects to a circle in R3. We use this approach
ON DIFFEOMORPHISMS OVER SURFACES IN THE COMPLEX PROJECTIVE PLANE
, 2004
"... Let M be a smooth closed oriented 4manifold (possibly with boundary) and F be a smooth closed oriented 2manifold (possibly with boundary) embedded in M. An orientation preserving diffeomorphism ψ over F is extendable if there is an orientation preserving diffeomorphism Ψ over M such that ΨF = ψ. ..."
Abstract
 Add to MetaCart
Let M be a smooth closed oriented 4manifold (possibly with boundary) and F be a smooth closed oriented 2manifold (possibly with boundary) embedded in M. An orientation preserving diffeomorphism ψ over F is extendable if there is an orientation preserving diffeomorphism Ψ over M such that ΨF = ψ. In general, for an oriented manifold A and its submanifold B, we denote Diff+(A, fix B) = orientation preserving diffeomorphisms ψ over A such that ψB = idB The group pi0(Diff+(F, fix ∂F)) is called the mapping class group of F and denoted by MF. If F is a closed oriented surface of genus g, this group is denoted by Mg. We define E(M,F) = {ϕ ∈MF  ϕ is extendable}. This is a subgroup of MF and is a central object of this note. 2. Surfaces in the 4sphere In this section, we review some known facts on E(S4, F) for the surface embedded in S4. A 3dimensional handlebody Hg is an oriented 3manifold which is constructed from a 3ball with attaching g 1handles. Any image of embeddings of Hg into S 4 are isotopic each other. Therefore, (S4, ∂Hg) is unique. A surface standardly (or trivially)embedded in S4 is (S4, ∂Hg). In [10] (the case where g = 1) and [5](the case where g = 2), we showed: Theorem 2.1. An orientation preserving diffeomorphism φ on ∂Hg is extendable to S4 if and only if φ preserves the Rokhlin quadratic from (i.e. the spin structure on ∂Hg induced from S
HAMILTONIAN STABILITY AND INDEX OF MINIMAL LAGRANGIAN SURFACES OF THE COMPLEX PROJECTIVE PLANE
, 2005
"... Abstract. We show that the Clifford torus and the totally geodesic real projective plane RP 2 in the complex projective plane CP 2 are the unique Hamiltonian stable minimal Lagrangian compact surfaces of CP 2 with genus g ≤ 4, when the surface is orientable, and with Euler characteristic χ ≥ −1, whe ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Abstract. We show that the Clifford torus and the totally geodesic real projective plane RP 2 in the complex projective plane CP 2 are the unique Hamiltonian stable minimal Lagrangian compact surfaces of CP 2 with genus g ≤ 4, when the surface is orientable, and with Euler characteristic χ ≥ −1
Results 1  10
of
36,761