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H-anti-invariant submersions from almost quaternionic Hermitian manifolds

Kwang-Soon Park (2017)

Czechoslovak Mathematical Journal

As a generalization of anti-invariant Riemannian submersions and Lagrangian Riemannian submersions, we introduce the notions of h-anti-invariant submersions and h-Lagrangian submersions from almost quaternionic Hermitian manifolds onto Riemannian manifolds. We obtain characterizations and investigate some properties: the integrability of distributions, the geometry of foliations, and the harmonicity of such maps. We also find a condition for such maps to be totally geodesic and give some examples...

H-conformal anti-invariant submersions from almost quaternionic Hermitian manifolds

Kwang Soon Park (2020)

Czechoslovak Mathematical Journal

We introduce the notions of h-conformal anti-invariant submersions and h-conformal Lagrangian submersions from almost quaternionic Hermitian manifolds onto Riemannian manifolds as a generalization of Riemannian submersions, horizontally conformal submersions, anti-invariant submersions, h-anti-invariant submersions, h-Lagrangian submersion, conformal anti-invariant submersions. We investigate their properties: the integrability of distributions, the geometry of foliations, the conditions for such...

Homotopie régulière inactive et engouffrement symplectique

François Laudenbach (1986)

Annales de l'institut Fourier

Une homotopie régulière ϕ t : Δ ( M , ω ) , t [ 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 U est déformable en une homotopie régulière inactive. On donne une application à l’engouffrement en géométrie symplectique.

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 ( 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 ( m + 2 ) and prove non-existence of real hypersurfaces in G 2 ( m + 2 ) with generalized Tanaka-Webster...

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