A new characterization of the sphere in $R^3$

Thomas Hasanis. "A new characterization of the sphere in $R^3$." Annales Polonici Mathematici 38.1 (1980): 47-49. <http://eudml.org/doc/265975>.

@article{ThomasHasanis1980,
abstract = {Let M be a closed connected surface in $R^3$ with positive Gaussian curvature K and let $K_II$ be the curvature of its second fundamental form. It is shown that M is a sphere if $K_II = c√HK^r$, for some constants c and r, where H is the mean curvature of M.},
author = {Thomas Hasanis},
journal = {Annales Polonici Mathematici},
keywords = {characterization of the sphere; Gaussian curvature; curvature of its second fundamental form},
language = {eng},
number = {1},
pages = {47-49},
title = {A new characterization of the sphere in $R^3$},
url = {http://eudml.org/doc/265975},
volume = {38},
year = {1980},
}

TY - JOUR
AU - Thomas Hasanis
TI - A new characterization of the sphere in $R^3$
JO - Annales Polonici Mathematici
PY - 1980
VL - 38
IS - 1
SP - 47
EP - 49
AB - Let M be a closed connected surface in $R^3$ with positive Gaussian curvature K and let $K_II$ be the curvature of its second fundamental form. It is shown that M is a sphere if $K_II = c√HK^r$, for some constants c and r, where H is the mean curvature of M.
LA - eng
KW - characterization of the sphere; Gaussian curvature; curvature of its second fundamental form
UR - http://eudml.org/doc/265975
ER -