2-Ruled Hypersurfaces in a Walker 4-Manifold

TL;DR

This paper introduces three types of 2-ruled hypersurfaces in a Walker 4-manifold, deriving their curvature properties, minimality conditions, and Laplace-Beltrami operators to advance geometric understanding.

Contribution

It defines and analyzes three new types of 2-ruled hypersurfaces in Walker 4-manifolds, providing curvature formulas and minimality characterizations.

Findings

Derived Gaussian and mean curvatures for the hypersurface types

Characterized conditions for minimality of these hypersurfaces

Analyzed Laplace-Beltrami operators on the hypersurfaces

Abstract

The hypersurface is one of the most important objects in a space. Many authors studied diffrent geometric aspects of hypersurfaces in a space. In this paper, we define three types of 2-ruled hypersurfaces in a Walker 4-manfold E 41 . We obtain the Gaussian and mean curvatures of the 2-ruled hypersurfaces of type-1, type-2 and type 3. We give some characterizations about its minimality. We also deal with the first Laplace-Beltrami operators of these types of 2-ruled hypersurfaces in the considered Walker 4-manifold.