Taiwanese Journal of Mathematics

Characterizations of Umbilic Points of Isometric Immersions in Riemannian and Lorentzian Manifolds

Magdalena Caballero and Rafael María Rubio

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Several characterizations of umbilic points of submanifolds in arbitrary Riemannian and Lorentzian manifolds are given. As a consequence, we obtain new characterizations of spheres in the Euclidean space and of hyperbolic spaces in the Lorentz-Minkowski space. We also prove the Lorentzian version of a classical result by Cartan.

Article information

Taiwanese J. Math., Volume 20, Number 5 (2016), 1041-1052.

First available in Project Euclid: 1 July 2017

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Zentralblatt MATH identifier

Primary: 53B20: Local Riemannian geometry 53B30: Lorentz metrics, indefinite metrics 53B25: Local submanifolds [See also 53C40] 53C24: Rigidity results

Riemannian and Lorentzian manifolds spacelike and timelike submanifolds umbilic point submanifold totally geodesic at a point mean curvature vector field sphere hyperbolic space


Caballero, Magdalena; Rubio, Rafael María. Characterizations of Umbilic Points of Isometric Immersions in Riemannian and Lorentzian Manifolds. Taiwanese J. Math. 20 (2016), no. 5, 1041--1052. doi:10.11650/tjm.20.2016.7383. https://projecteuclid.org/euclid.twjm/1498874515

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