Results 21 to 30 of about 179 (133)
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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Totally Umbilical Lightlike Hypersurfaces in Robertson-Walker Spacetimes [PDF]
ISRN Geometry, 2014 We study the problem of lightlike hypersurface immersed into Robertson-Walker (RW) spacetimes in this paper, where the screen bundle of the hypersurface has constant higher order mean curvature. We consider the following question: under what conditions is the compact lightlike hypersurface totally umbilical?
Dong, Junhong, Liu, Ximin
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Characterization of totally umbilical hypersurfaces [PDF]
Proceedings of the American Mathematical Society, 1981 This paper gives a sufficient condition for a complete hypersurface of a Riemannian manifold of constant curvature to be umbilical. The condition will be given by an inequality which is established between the length of the second fundamental tensor and the mean curvature. K. Nomizu and B.
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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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On C^2 Umbilical Hypersurfaces
, 2022 We show by an elementary argument that the second fundamental form of a connected, totally umbilical hypersurface of class C2 is a constant multiple of the metric tensor. It follows that the hypersurface is smooth and it is either a piece of a hyperplane
carlo mantegazza
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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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Quasi‐Einstein Hypersurfaces of Complex Space Forms
Advances in Mathematical Physics, Volume 2020, Issue 1, 2020., 2020 Based on a well‐known fact that there are no Einstein hypersurfaces in a nonflat complex space form, in this article, we study the quasi‐Einstein condition, which is a generalization of an Einstein metric, on the real hypersurface of a nonflat complex space form. For the real hypersurface with quasi‐Einstein metric of a complex Euclidean space, we also
Xuehui Cui, Guozhen Lu, Xiaomin Chen
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