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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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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.
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참고문헌 (32)
참고문헌 신청
C. Burstin / 1927 / Uber affine Geometrie XLI ¨ : Die Geometrie zweifach ausgedehnter Mannigfaltigkeiten F2 im affinen R4 / Math. Z 26(1):373~407
B.-Y. Chen / 1973 / Geometry of submanifolds / Marcel Dekker, Inc
B.-Y. Chen / 1980 / Surfaces with parallel normalized mean curvature vector / Monatsh. Math 90(3):185~194
B.-Y. Chen / 2008 / Classification of marginally trapped Lorentzian flat surfaces in E 42and its application to biharmonic surfaces / J. Math. Anal. Appl 340(2):861~875
B.-Y. Chen / 2009 / Classification of marginally trapped surfaces of constant curvature in Lorentzian complex plane / Hokkaido Math. J 38(2):361~408
B.-Y. Chen / 1973 / Geometry of submanifolds / Marcel Dekker, Inc
B.-Y. Chen / 1980 / Surfaces with parallel normalized mean curvature vector / Monatsh. Math 90(3):185~194
B.-Y. Chen / 2008 / Classification of marginally trapped Lorentzian flat surfaces in E 42and its application to biharmonic surfaces / J. Math. Anal. Appl 340(2):861~875
B.-Y. Chen / 2009 / Classification of marginally trapped surfaces of constant curvature in Lorentzian complex plane / Hokkaido Math. J 38(2):361~408
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