TITLE:
Biconservative Submanifolds in 5-Dimensional Pseudo-Euclidean Space
AUTHORS:
Yaqi Guo
KEYWORDS:
Pseudo-Euclidean Space Form, Principal Curvatures, Proper Biconservative, Scalar Curvature
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.16 No.5,
May
27,
2026
ABSTRACT: This paper focuses on the geometric rigidity of 3-dimensional proper biconservative submanifolds
M
r
3
with a parallel normalized mean curvature vector field in the 5-dimensional pseudo-Euclidean space
E
s
5
. Grounded in the theories of harmonic maps, biharmonic maps, and stress-energy tensors, we employ fundamental tools from pseudo-Riemannian geometry including the Gauss equation, Weingarten formula, and Codazzi equation to derive the equivalent conditions characterizing biconservative submanifolds. We further establish that if the shape operator of such a submanifold is diagonalizable and admits at most two distinct principal curvatures in the direction of the mean curvature vector field
H
, its scalar curvature takes the form of a fractional-power polynomial in the mean curvature
f
with non-vanishing coefficients. In particular, any such submanifold with constant scalar curvature necessarily possesses constant mean curvature, revealing a striking rigidity property.