A certain complete space-like hypersurface in Lorentz manifolds.
A characterization of the Grassmann manifold . Another review.
A characterization of totally -umbilical real hypersurfaces and ruled real hypersurfaces of a complex space form
We give a characterization of totally -umbilical real hypersurfaces and ruled real hypersurfaces of a complex space form in terms of totally umbilical condition for the holomorphic distribution on real hypersurfaces. We prove that if the shape operator of a real hypersurface of a complex space form , , , satisfies for any , being a function, where is the holomorphic distribution on , then is a totally -umbilical real hypersurface or locally congruent to a ruled real hypersurface....
A class of 3-dimensional almost Kenmotsu manifolds with harmonic curvature tensors
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 class of locally symmetric Kähler Einstein structures on the nonzero cotangent bundle of a space form.
A classification of contact metric 3-manifolds with constant -sectional and -sectional curvatures.
A classification of the torsion tensors on almost contact manifolds with B-metric
The space of the torsion (0,3)-tensors of the linear connections on almost contact manifolds with B-metric is decomposed in 15 orthogonal and invariant subspaces with respect to the action of the structure group. Three known connections, preserving the structure, are characterized regarding this classification.
A curvature identity on a 6-dimensional Riemannian manifold and its applications
We derive a curvature identity that holds on any 6-dimensional Riemannian manifold, from the Chern-Gauss-Bonnet theorem for a 6-dimensional closed Riemannian manifold. Moreover, some applications of the curvature identity are given. We also define a generalization of harmonic manifolds to study the Lichnerowicz conjecture for a harmonic manifold “a harmonic manifold is locally symmetric” and provide another proof of the Lichnerowicz conjecture refined by Ledger for the 4-dimensional case under a...
A discreteness criterion for the spectrum of the Laplace--Beltrami operator on quasimodel manifolds.
A Frankel type theorem for CR submanifolds of Sasakian manifolds
We prove a Frankel type theorem for submanifolds of Sasakian manifolds, under suitable hypotheses on the index of the scalar Levi forms determined by normal directions. From this theorem we derive some topological information about submanifolds of Sasakian space forms.
A Function Defined on an Even-dimensional Real Submanifold of a Hermitian Manifold
A Geometric Property of Central Elements.
A Kähler Einstein structure on the tangent bundle of a space form.
A locally symmetric Kähler Einstein structure on the cotangent bundle of a space form.
A locally symmetric Kähler Einstein structure on the tangent bundle of a space form.
A new example of compact Riemannian manifold with structure group Spin(7)
A new variational characterization of compact conformally flat 4-manifolds
In this paper, we give a new variational characterization of certain 4-manifolds. More precisely, let and denote the scalar curvature and Ricci curvature respectively of a Riemannian metric, we prove that if is compact and locally conformally flat and is the critical point of the functional where
A nonlinear Poisson transform for Einstein metrics on product spaces
We consider the Einstein deformations of the reducible rank two symmetric spaces of noncompact type. If is the product of any two real, complex, quaternionic or octonionic hyperbolic spaces, we prove that the family of nearby Einstein metrics is parametrized by certain new geometric structures on the Furstenberg boundary of .
A note on a hermitian analog of Einstein spaces
A note on Chen's basic equality for submanifolds in a Sasakian space form.