2024 : 11 : 13
Firooz Pashaie

Firooz Pashaie

Academic rank: Associate Professor
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Education: PhD.
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Faculty: 1
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Research

Title
ON TIMELIKE HYPERSURFACES OF THE MINKOWSKI 4-SPACE WITH 1-PROPER SECOND MEAN CURVATURE VECTOR
Type
JournalPaper
Keywords
Weak convex, Lorentz hypersurface, Biharmonic, C-harmonic
Year
2022
Journal journal of mahani mathematical research
DOI
Researchers Firooz Pashaie ، ، Asghar Rahimi ، Leila Shahbaz

Abstract

The mean curvature vector field of a submanifold in the Eu- clidean n-space is said to be proper if it is an eigenvector of the Laplace operator ∆. It is proven that every hypersurface with proper mean cur- vature vector field in the Euclidean 4-space E4 has constant mean cur- vature. In this paper, we study an extended version of the mentioned subject on timelike (i.e., Lorentz) hypersurfaces of Minkowski 4-space E4 1. Let x : M 3 1 → E4 1 be the isometric immersion of a timelike hyper- surface M 3 1 in E4 1. The second mean curvature vector field H2 of M 3 1 is called 1-proper if it is an eigenvector of the Cheng-Yau operator C (which is the natural extension of ∆). We show that each M 3 1 with 1-proper H2 has constant scalar curvature. By a classification theorem, we show that such a hypersurface is C-biharmonic, C-1-type or null-C-2-type. Since the shape operator of M 3 1 has four possible matrix forms, the results will be considered in four different cases.