Results 21 to 30 of about 17,898 (118)
Pythagorean Isoparametric Hypersurfaces in Riemannian and Lorentzian Space Forms
Axioms, 2022 We introduce the notion of a Pythagorean hypersurface immersed into an n+1-dimensional pseudo-Riemannian space form of constant sectional curvature c∈−1,0,1.
Muhittin Evren Aydın +2 more
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On a property of W4 -manifolds
Дифференциальная геометрия многообразий фигур, 2020 The properties of almost Hermitian manifolds belonging to the Gray — Hervella class W4 are considered. The almost Hermitian manifolds of this class were studied by such outstanding geometers like Alfred Gray, Izu Vaisman, and Vadim Feodorovich Kirichenko.
M.B. Banaru
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Some New Results on Trans‐Sasakian Manifolds
Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022 In this paper, we classify trans‐Sasakian manifolds which are realized as real hypersurfaces in a complex space form. We also investigate trans‐Sasakian manifolds whose Reeb vector fields are harmonic‐Killing. The above results bring some new characterizations for the property of trans‐Sasakian 3‐manifolds.
Lei Wang, Yan Zhao, Antonio Masiello
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CONFORMAL VECTOR FIELDS AND TOTALLY UMBILIC HYPERSURFACES [PDF]
Bulletin of the Korean Mathematical Society, 2002 Let \((M^n,g)\), \(n\geq 2\), be a connected semi-Riemannian hypersurface of a semi-Riemannian space form \((\overline{M}_k^{n+1}(\overline{c}),\overline{g})\) of signature \(k\). Assume that the ambient manifold carries a conformal vector field \(V\) such that the tangential part \((V|M^n)^T\) becomes a conformal vector field on the hypersurface. Then
Kim, Dong-Soo +3 more
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A Variational Problem and Classification Theorem for Extremal Hypersurfaces in the Space Form
Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022 The classification of the isoparametric extremal hypersurfaces in the space form is obtained in this paper. We also derived the Euler‐Lagrange equation for extremal hypersurface and obtained Simons’ type integral inequality. When the integral equality holds, we can obtain the characteristics of isoparametric extremal hypersurfaces by using this ...
Yu-Chung Chang, Efthymios G. Tsionas
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Uniqueness of Complete Hypersurfaces in Weighted Riemannian Warped Products
Advances in Mathematical Physics, Volume 2021, Issue 1, 2021., 2021 In this paper, applying the weak maximum principle, we obtain the uniqueness results for the hypersurfaces under suitable geometric restrictions on the weighted mean curvature immersed in a weighted Riemannian warped product I×ρMfn whose fiber M has f‐parabolic universal covering. Furthermore, applications to the weighted hyperbolic space are given. In
Ning Zhang, Leopoldo Greco
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New Bernstein Type Results in Weighted Warped Products
Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021 In this paper, we obtain new parametric uniqueness results for complete constant weighted mean curvature hypersurfaces under suitable geometric assumptions in weighted warped products. Furthermore, we also prove very general Bernstein type results for the constant mean curvature equation for entire graphs in these ambient spaces.
Ning Zhang, Yongqiang Fu
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Hypersurfaces of a Sasakian manifold - revisited
Journal of Inequalities and Applications, 2021 We study orientable hypersurfaces in a Sasakian manifold. The structure vector field ξ of a Sasakian manifold determines a vector field v on a hypersurface that is the component of the Reeb vector field ξ tangential to the hypersurface, and it also gives
Sharief Deshmukh +3 more
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Hiroshima Mathematical Journal, 1990 Let M be a complete hypersurface with constant mean curvature of a space form of index s \((=0\) or 1). A sufficient condition, which is established between the length of the second fundamental form and the mean curvature, is given for M to be totally umbilical. This result generalizes the reviewer's result [Proc. Am. Math. Soc.
Cheng, Qing Ming, Nakagawa, Hisao
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NOTES ON MANIFOLDS ADMITTING TOTALLY UMBILICAL HYPERSURFACES
Demonstratio Mathematica, 1987 Let N be either a conformally recurrent manifold [see \textit{T. Adati} and \textit{T. Miyazawa}, Tensor, New Ser. 18, 335-342 (1967; Zbl 0152.391)] or a conformally birecurrent manifold [see \textit{C. D. Collinson} and \textit{F. Söler} [ibid. 27, 37-40 (1973; Zbl 0251.53039)], i.e.
Deszcz, Ryszard +1 more
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