Year: 2023
Type: preprint
Abstract: In this paper, we study $λ$-submanifolds of arbitrary codimensions in Gauss spaces. These submanifolds can be seen as natural generalizations of self-shrinker and $λ$-hypersurfaces. Using a divergence type theorem and some Simons' type identities, we prove some halfspace type theorems and gap theorems for complete proper $λ$-submanifolds. These generalized our as well as the others' results for self-shrinker or $λ$-hypersurfaces to $λ$-submanifolds.
Source: arXiv (Cornell University)
Author: Hieu, Doan The
Institutions: Hue University, Hue University of Education
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4366563818