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Homomorphisms of the Lie algebras associated with a symplectic manifold

C. J. Atkin, J. Grabowski (1990)

Compositio Mathematica

Homotopie rationnelle et croissance du nombre de géodésiques fermées

Micheline Vigué-Poirrier (1984)

Annales scientifiques de l'École Normale Supérieure

Homotopie régulière inactive et engouffrement symplectique

François Laudenbach (1986)

Annales de l'institut Fourier

Une homotopie régulière $ϕ_{t} : Δ \to (M, ω)$ , $t \in [0, 1]$ , dans une variété symplectique est dite inactive si en chaque point le déplacement infinitésimal est $ω$ -orthogonal à l’espace tangent de l’objet déplacé. Si $Δ$ est un polyèdre de $M^{2 n}$ de dimension $< n$ et si $U$ est un ouvert de $M$ , toute homotopie de $Δ ↪ M$ jusqu’à $Δ \to U$ est déformable en une homotopie régulière inactive. On donne une application à l’engouffrement en géométrie symplectique.

Homotopien von Untermannigfaltigkeiten mit nicht ausgearteter zweiter Fundamentalform

Peter Wintgen (1975)

Czechoslovak Mathematical Journal

Homotopy algebras via resolutions of operads

Markl, Martin (2000)

Proceedings of the 19th Winter School "Geometry and Physics"

Summary: All algebraic objects in this note will be considered over a fixed field $k$ of characteristic zero. If not stated otherwise, all operads live in the category of differential graded vector spaces over $k$ . For standard terminology concerning operads, algebras over operads, etc., see either the original paper by J. P. May [“The geometry of iterated loop spaces”, Lect. Notes Math. 271 (1972; Zbl 0244.55009)], or an overview [J.-L. Loday, “La renaissance des opérads”, Sémin. Bourbaki 1994/95,...

Homotopy Classification of Nondegenerate Quasiperiodic Curves on the 2-sphere

B. Z. Shapiro, B. A. Khesin (1999)

Publications de l'Institut Mathématique

Homotopy classification of regular sections

Andrew du Plessis (1976)

Compositio Mathematica

Homotopy diagrams of algebras

Markl, Martin (2002)

Proceedings of the 21st Winter School "Geometry and Physics"

The paper is concerned with homotopy concepts in the category of chain complexes. It is part of the author’s program to translate [J. M. Boardman and R. M. Vogt, Homotopy invariant algebraic structures on topological spaces, Lect. Notes Math. 347, Springer-Verlag (1973; Zbl 0285.55012)] from topology to algebra.In topology the notion of operad extracts the essential algebraic information contained in the following example (endomorphism operad).The endomorphism operad $ℰ_{X}$ of a based space $X$ consists...

Homotopy properties of Hamiltonian group actions.

Kȩdra, Jarek, McDuff, Dusa (2005)

Geometry & Topology

Homotopy theory and circle actions on symplectic manifolds

John Oprea (1998)

Banach Center Publications

Homotopy type of Euclidean configuration spaces

Salvatore, Paolo (2001)

Proceedings of the 20th Winter School "Geometry and Physics"

Let $F (ℝ^{n}, k)$ denote the configuration space of pairwise-disjoint $k$ -tuples of points in $ℝ^{n}$ . In this short note the author describes a cellular structure for $F (ℝ^{n}, k)$ when $n \geq 3$ . From results in [F. R. Cohen, T. J. Lada and J. P. May, The homology of iterated loop spaces, Lect. Notes Math. 533 (1976; Zbl 0334.55009)], the integral (co)homology of $F (ℝ^{n}, k)$ is well-understood. This allows an identification of the location of the cells of $F (ℝ^{n}, k)$ in a minimal cell decomposition. Somewhat more detail is provided by the main result here,...

Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster $𝔇^{⊥}$ -parallel structure Jacobi operator

Eunmi Pak, Young Suh (2014)

Open Mathematics

Regarding the generalized Tanaka-Webster connection, we considered a new notion of $𝔇^{⊥}$ -parallel structure Jacobi operator for a real hypersurface in a complex two-plane Grassmannian G 2(ℂm+2) and proved that a real hypersurface in G 2(ℂm+2) with generalized Tanaka-Webster $𝔇^{⊥}$ -parallel structure Jacobi operator is locally congruent to an open part of a tube around a totally geodesic quaternionic projective space ℍP n in G 2(ℂm+2), where m = 2n.

Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster parallel normal Jacobi operator

Eunmi Pak, Juan de Dios Pérez, Carlos J. G. Machado, Changhwa Woo (2015)

Czechoslovak Mathematical Journal

We study the classifying problem of immersed submanifolds in Hermitian symmetric spaces. Typically in this paper, we deal with real hypersurfaces in a complex two-plane Grassmannian $G_{2} (ℂ^{m + 2})$ which has a remarkable geometric structure as a Hermitian symmetric space of rank 2. In relation to the generalized Tanaka-Webster connection, we consider a new concept of the parallel normal Jacobi operator for real hypersurfaces in $G_{2} (ℂ^{m + 2})$ and prove non-existence of real hypersurfaces in $G_{2} (ℂ^{m + 2})$ with generalized Tanaka-Webster...

Hopf hypersurfaces in nearly Kaehler 6-sphere.

Deshmukh, Sharief, Al-Solamy, Falleh R. (2008)

Balkan Journal of Geometry and its Applications (BJGA)

Hopf structures on the Borel subalgebra of $s l (2)$

Ogievetsky, O. (1994)

Proceedings of the Winter School "Geometry and Physics"

Horizons in five-dimensional theory

J.-P. Duruisseau (1977)

Annales de l'I.H.P. Physique théorique

Horizontal and contact forms on constraint manifolds

Krupková, Olga, Swaczyna, Martin (2005)

Proceedings of the 24th Winter School "Geometry and Physics"

Horizontal and vertical geodesics in the Riemann space

I. Čomić (1990)

Matematički Vesnik

Horizontal forms of Chern type on complex Finsler bundles.

Ida, Cristian (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Horizontal lift of symmetric connections to the bundle of volume forms ν

Anna Gąsior (2010)

Annales UMCS, Mathematica

In this paper we present the horizontal lift of a symmetric affine connection with respect to another affine connection to the bundle of volume forms ν and give formulas for its curvature tensor, Ricci tensor and the scalar curvature. Next, we give some properties of the horizontally lifted vector fields and certain infinitesimal transformations. At the end, we consider some substructures of a F(3, 1)-structure on ν.

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