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If $(M, \nabla)$ is a manifold with a symmetric linear connection, then $T^{*} M$ can be endowed with the natural Riemann extension $\bar{g}$ (O. Kowalski and M. Sekizawa (2011), M. Sekizawa (1987)). Here we continue to study the harmonicity with respect to $\bar{g}$ initiated by C. L. Bejan and O. Kowalski (2015). More precisely, we first construct a canonical almost para-complex structure $𝒫$ on $(T^{*} M, \bar{g})$ and prove that $𝒫$ is harmonic (in the sense of E. García-Río, L. Vanhecke and M. E. Vázquez-Abal (1997)) if and only if $\bar{g}$ reduces to the...

A characterization of totally $η$ -umbilical real hypersurfaces and ruled real hypersurfaces of a complex space form

Mayuko Kon (2008)

Czechoslovak Mathematical Journal

We give a characterization of totally $η$ -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 $A$ of a real hypersurface $M$ of a complex space form $M^{n} (c)$ , $c \neq 0$ , $n \geq 3$ , satisfies $g (A X, Y) = a g (X, Y)$ for any $X, Y \in T_{0} (x)$ , $a$ being a function, where $T_{0}$ is the holomorphic distribution on $M$ , then $M$ is a totally $η$ -umbilical real hypersurface or locally congruent to a ruled real hypersurface....

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 class of boundary problems for extremal surfaces of mixed type in Minkowski 3-space.

Chaohao Gu (1988)

Journal für die reine und angewandte Mathematik

A class of complex hypersurfaces

Patrick J. Ryan (1972)

Colloquium Mathematicae

A class of discriminant varieties in the conformal 3-sphere.

Baird, Paul, Gallardo, Luis (2002)

Beiträge zur Algebra und Geometrie

A class of locally symmetric Kähler Einstein structures on the nonzero cotangent bundle of a space form.

Poroşniuc, Dumitru Daniel (2004)

Balkan Journal of Geometry and its Applications (BJGA)

A class of metrics on tangent bundles of pseudo-Riemannian manifolds

H. M. Dida, A. Ikemakhen (2011)

Archivum Mathematicum

We provide the tangent bundle $T M$ of pseudo-Riemannian manifold $(M, g)$ with the Sasaki metric $g^{s}$ and the neutral metric $g^{n}$ . First we show that the holonomy group $H^{s}$ of $(T M, g^{s})$ contains the one of $(M, g)$ . What allows us to show that if $(T M, g^{s})$ is indecomposable reducible, then the basis manifold $(M, g)$ is also indecomposable-reducible. We determine completely the holonomy group of $(T M, g^{n})$ according to the one of $(M, g)$ . Secondly we found conditions on the base manifold under which $(T M, g^{s})$ ( respectively $(T M, g^{n})$ ) is Kählerian, locally symmetric or Einstein...

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A Characterization of the Cannonical Spheres by the Spectrum.

A characterization of the Grassmann manifold $G_{p, 2} (ℝ)$ . Another review.

A Characterization of the Hopf Map by Stretch.

A characterization of the Riemann extension in terms of harmonicity

A characterization of totally $η$ -umbilical real hypersurfaces and ruled real hypersurfaces of a complex space form

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

A class of boundary problems for extremal surfaces of mixed type in Minkowski 3-space.

A class of complex hypersurfaces

A class of discriminant varieties in the conformal 3-sphere.

A class of locally symmetric Kähler Einstein structures on the nonzero cotangent bundle of a space form.

A class of metrics on tangent bundles of pseudo-Riemannian manifolds

A Class of Non-Polarizable Symplectic Manifolds.

A class of projectively flat surfaces.

A class of self-concordant functions on Riemannian manifolds.

A class of symmetric spaces

A class of tight contact structures on $Σ_{2} \times I$ .

A classfication of 3-type curves in Minkowski 3-space $E_{1}^{3}$ . II.

A classification of 2-type curves in the Minkowski space $𝔼_{1}^{n}$ .

A Classification of 2-type Curves in the Minkowski Space E1n

A classification of 3-type curves in Minkowski 3-space $E_{1}^{3}$ . I.

Currently displaying 41 – 60 of 776