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On the theory of Lorentz surfaces with parallel normalized mean curvature vector field in pseudo-Euclidean 4-space

Georgi Ganchev|Velichka Milousheva|Yana Aleksieva
대한수학회 (The Korean Mathematical Society)|2016.09|대한수학회지 (Journal of the KMS)|제53권 제5호|pp. 1077-1100

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참고문헌

키워드

Lorentz surfacefundamental existence and uniqueness theoremparallel normalized mean curvature vectorcanonical parameters
주제분류수학

초록

We develop an invariant local theory of Lorentz surfaces in pseudo-Euclidean 4-space by use of a linear map of Weingarten type. We find a geometrically determined moving frame field at each point of the surface and obtain a system of geometric functions. We prove a fundamental existence and uniqueness theorem in terms of these functions. On any Lorentz surface with parallel normalized mean curvature vector field we introduce special geometric (canonical) parameters and prove that any such surface is determined up to a rigid motion by three invariant functions satisfying three natural partial differential equations. In this way we minimize the number of functions and the number of partial differential equations determining the surface, which solves the Lund-Regge problem for this class of surfaces.

Abstract

We develop an invariant local theory of Lorentz surfaces in pseudo-Euclidean 4-space by use of a linear map of Weingarten type. We find a geometrically determined moving frame field at each point of the surface and obtain a system of geometric functions. We prove a fundamental existence and uniqueness theorem in terms of these functions. On any Lorentz surface with parallel normalized mean curvature vector field we introduce special geometric (canonical) parameters and prove that any such surface is determined up to a rigid motion by three invariant functions satisfying three natural partial differential equations. In this way we minimize the number of functions and the number of partial differential equations determining the surface, which solves the Lund-Regge problem for this class of surfaces.

참고문헌 (32)

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