A by-proxy talk on Alexandrov's contribution.
Kutateladze, S. S. (2002)
Vladikavkazskiĭ Matematicheskiĭ Zhurnal
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Displaying similar documents to “Total mean curvature and closed geodesics.”
A by-proxy talk on Alexandrov's contribution.
A characterization of regular saddle surfaces in the hyperbolic and spherical three-space.
Kalikakis, Dimitrios E. (2002)
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On the curvature of nonregular saddle surfaces in the hyperbolic and spherical three-space.
Kalikakis, Dimitrios E. (2002)
Abstract and Applied Analysis
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Surfaces of characteristic curvature
Vladimír Fiřt (1974)
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Prescribing Gauss curvature of surfaces in 3-dimensional spacetimes Application to the Minkowski problem in the Minkowski space
Thierry Barbot, François Béguin, Abdelghani Zeghib (2011)
Annales de l’institut Fourier
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We study the existence of surfaces with constant or prescribed Gauss curvature in certain Lorentzian spacetimes. We prove in particular that every (non-elementary) 3-dimensional maximal globally hyperbolic spatially compact spacetime with constant non-negative curvature is foliated by compact spacelike surfaces with constant Gauss curvature. In the constant negative curvature case, such a foliation exists outside the convex core. The existence of these foliations, together with a theorem...
Some inequalities for immersed surfaces.
Marenich, V., Guadalupe, I.V. (1997)
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Invariants and Bonnet-type theorem for surfaces in ℝ4
Georgi Ganchev, Velichka Milousheva (2010)
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In the tangent plane at any point of a surface in the four-dimensional Euclidean space we consider an invariant linear map ofWeingarten-type and find a geometrically determined moving frame field. Writing derivative formulas of Frenet-type for this frame field, we obtain eight invariant functions. We prove a fundamental theorem of Bonnet-type, stating that these eight invariants under some natural conditions determine the surface up to a motion. We show that the basic geometric classes...
Complete classification of spatial surfaces with parallel mean curvature vector in arbitrary non-flat pseudo-Riemannian space forms
Bang-Yen Chen (2009)
Open Mathematics
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Submanifolds with parallel mean curvature vector play important roles in differential geometry, theory of harmonic maps as well as in physics. Spatial surfaces in 4D Lorentzian space forms with parallel mean curvature vector were classified by B. Y. Chen and J. Van der Veken in [9]. Recently, spatial surfaces with parallel mean curvature vector in arbitrary pseudo-Euclidean spaces are also classified in [7]. In this article, we classify spatial surfaces with parallel mean curvature vector...