A pointwise inequality in submanifold theory

P. J. De Smet; F. Dillen; Leopold C. A. Verstraelen; L. Vrancken

Archivum Mathematicum (1999)

  • Volume: 035, Issue: 2, page 115-128
  • ISSN: 0044-8753

Abstract

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We obtain a pointwise inequality valid for all submanifolds M n of all real space forms N n + 2 ( c ) with n ≥ 2 and with codimension two, relating its main scalar invariants, namely, its scalar curvature from the intrinsic geometry of M n , and its squared mean curvature and its scalar normal curvature from the extrinsic geometry of M n in N m ( c ) .

How to cite

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De Smet, P. J., et al. "A pointwise inequality in submanifold theory." Archivum Mathematicum 035.2 (1999): 115-128. <http://eudml.org/doc/248351>.

@article{DeSmet1999,
abstract = {We obtain a pointwise inequality valid for all submanifolds $M^n$ of all real space forms $N^\{n+2\}(c)$ with $n\ge 2$ and with codimension two, relating its main scalar invariants, namely, its scalar curvature from the intrinsic geometry of $M^n$, and its squared mean curvature and its scalar normal curvature from the extrinsic geometry of $M^n$ in $N^m(c)$.},
author = {De Smet, P. J., Dillen, F., Verstraelen, Leopold C. A., Vrancken, L.},
journal = {Archivum Mathematicum},
keywords = {submanofolds of real space froms; scalar curvature; normal curvature; mean curvature; inequality; submanifolds of real space forms; scalar curvature; normal curvature; mean curvature; inequality},
language = {eng},
number = {2},
pages = {115-128},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {A pointwise inequality in submanifold theory},
url = {http://eudml.org/doc/248351},
volume = {035},
year = {1999},
}

TY - JOUR
AU - De Smet, P. J.
AU - Dillen, F.
AU - Verstraelen, Leopold C. A.
AU - Vrancken, L.
TI - A pointwise inequality in submanifold theory
JO - Archivum Mathematicum
PY - 1999
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 035
IS - 2
SP - 115
EP - 128
AB - We obtain a pointwise inequality valid for all submanifolds $M^n$ of all real space forms $N^{n+2}(c)$ with $n\ge 2$ and with codimension two, relating its main scalar invariants, namely, its scalar curvature from the intrinsic geometry of $M^n$, and its squared mean curvature and its scalar normal curvature from the extrinsic geometry of $M^n$ in $N^m(c)$.
LA - eng
KW - submanofolds of real space froms; scalar curvature; normal curvature; mean curvature; inequality; submanifolds of real space forms; scalar curvature; normal curvature; mean curvature; inequality
UR - http://eudml.org/doc/248351
ER -

References

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