Generalized Helical Hypersurface with Space-like Axis in Minkowski 5-Space
نویسندگان
چکیده
We introduce the generalized helical hypersurface having a space-like axis in five-dimensional Minkowski space. compute first and second fundamental form matrices, Gauss map, shape operator matrix of hypersurface. Additionally, we curvatures by using Cayley–Hamilton theorem. Moreover, give some relations for mean Gauss–Kronecker Finally, obtain Laplace–Beltrami
منابع مشابه
A Generalized Clairaut’s Theorem in Minkowski Space
In Euclidean space, the geodesics on a surface of revolution can be characterized by means of Clairaut’s theorem, which essentially says that the geodesics are curves of fixed angular momentum. A similar result is known for three dimensional Minkowski space for timelike geodesics on surfaces of revolution about the time axis. Here, we extend this result to consider generalizations of surfaces o...
متن کاملA certain complete space-like hypersurface in Lorentz manifolds
In this paper, we find an upper bound of the squared norm of the second fundamental tensor of a complete space-like hypersurface in a Lorentz space form M 1 (c) satisfying some curvature conditions . Then it gives naturally an extension of some theorems of Cheng and Nakagawa ([3]), Ishihara ([7]), Li ([8]) and Nishikawa ([9]). Mathematics Subject Classification: 53C50, 53C25, 53C42.
متن کاملTime-like Involutes of a space-like helix in Minkowski space-time
In this work, we deal with a classical differential geometry topic in Minkowski space-time. First, we prove that there are no timelike involutes of a time-like evolute. In the light of this result, we observed that involute curve transforms to a time-like curve when evolute is a space-like helix with a time-like principal normal. Then, we investigated relationships among Frenet-Serret apparatus...
متن کاملOn de Sitter-like and Minkowski-like space-times
Friedrich’s proofs for the global existence results of de Sitter-like space-times and of semiglobal existence of Minkowski-like space-times [Comm. Math. Phys. 107, 587 (1986)] are re-examined and discussed, making use of the extended conformal field equations and a gauge based on conformal geodesics. In this gauge the location of the conformal boundary of the space-times is known a priori once ...
متن کاملGeneralized Null 2-Type Surfaces in Minkowski 3-Space
For the mean curvature vector field H and the Laplace operator ∆ of a submanifold in the Minkowski space, a submanifold satisfying the condition ∆H = f H + gC is known as a generalized null 2-type, where f and g are smooth functions, and C is a constant vector. The notion of generalized null 2-type submanifolds is a generalization of null 2-type submanifolds defined by B.-Y. Chen. In this paper...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Universe
سال: 2023
ISSN: ['2218-1997']
DOI: https://doi.org/10.3390/universe9030152