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3-submersions from QR-hypersurfaces of quaternionic Kähler manifolds

Gabriel Eduard Vîlcu (2010)

Annales Polonici Mathematici

We study 3-submersions from a QR-hypersurface of a quaternionic Kähler manifold onto an almost quaternionic hermitian manifold. We also prove the non-existence of quaternionic submersions between quaternionic Kähler manifolds which are not locally hyper-Kähler.

A class of 3-dimensional almost Kenmotsu manifolds with harmonic curvature tensors

Yaning Wang (2016)

Open Mathematics

Let M3 be a three-dimensional almost Kenmotsu manifold satisfying ▽ξh = 0. In this paper, we prove that the curvature tensor of M3 is harmonic if and only if M3 is locally isometric to either the hyperbolic space ℍ3(-1) or the Riemannian product ℍ2(−4) × ℝ. This generalizes a recent result obtained by [Wang Y., Three-dimensional locally symmetric almost Kenmotsu manifolds, Ann. Polon. Math., 2016, 116, 79-86] and [Cho J.T., Local symmetry on almost Kenmotsu three-manifolds, Hokkaido Math. J., 2016,...

A classification of certain submanifolds of an S-manifold

José L. Cabrerizo, Luis M. Fernández, Manuel Fernández (1991)

Annales Polonici Mathematici

A classification theorem is obtained for submanifolds with parallel second fundamental form of an 𝑆-manifold whose invariant f-sectional curvature is constant.

A complete classification of four-dimensional paraKähler Lie algebras

Giovanni Calvaruso (2015)

Complex Manifolds

We consider paraKähler Lie algebras, that is, even-dimensional Lie algebras g equipped with a pair (J, g), where J is a paracomplex structure and g a pseudo-Riemannian metric, such that the fundamental 2-form Ω(X, Y) = g(X, JY) is symplectic. A complete classification is obtained in dimension four.

A contact metric manifold satisfying a certain curvature condition

Jong Taek Cho (1995)

Archivum Mathematicum

In the present paper we investigate a contact metric manifold satisfying (C) ( ¯ γ ˙ R ) ( · , γ ˙ ) γ ˙ = 0 for any ¯ -geodesic γ , where ¯ is the Tanaka connection. We classify the 3-dimensional contact metric manifolds satisfying (C) for any ¯ -geodesic γ . Also, we prove a structure theorem for a contact metric manifold with ξ belonging to the k -nullity distribution and satisfying (C) for any ¯ -geodesic γ .

A convex Darboux theorem

Pierre-André Chiappori, Ivar Ekeland (1997)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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