Open AccessISOMETRIC IMMERSION OF MINIMAL SPHERICAL SUBMANIFOLD VIA THE SECOND STANDARD IMMERSION OF THE SPHERE
Author(s) -
Xinmin Zhang
Publication year - 1992
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.23.1992.4537
Subject(s) - immersion (mathematics) , submanifold , mathematics , isometric exercise , unit sphere , mathematical analysis , pure mathematics , combinatorics , medicine , physical therapy
Let $M^n$ be a $n$-dimensional compact connected minimal submanifold of the unit sphere $S^{n+p}(1)$. In this paper we study the isometric immersion of $M^n$ into $SM(n +p + 1)$ via the second standard immersion of $S^{n+p}(1)$. We obtain some integral inequalities m terms of the spectrum of the Laplace operator of $M^n$ and find some restrictions on such immersions.