Geodesic
Mean curvature and shape operator of isometric immersions in real-space-forms
Glasgow mathematical journal, Tome 38 (1996) no. 1, pp. 87-97

Voir la notice de l'article provenant de la source Cambridge University Press

According to the well-known Nash's theorem, every Riemannian n-manifold admits an isometric immersion into the Euclidean space En(n+1)(3n+11)/2. In general, there exist enormously many isometric immersions from a Riemannian manifold into Euclidean spaces if no restriction on the codimension is made. For a submanifold of a Riemannian manifold there are associated several extrinsic invariants beside its intrinsic invariants. Among the extrinsic invariants, the mean curvature function and shape operator are the most fundamental ones. 
Chen, Bang-Yen. Mean curvature and shape operator of isometric immersions in real-space-forms. Glasgow mathematical journal, Tome 38 (1996) no. 1, pp. 87-97. doi: 10.1017/S001708950003130X
@article{10_1017_S001708950003130X,
     author = {Chen, Bang-Yen},
     title = {Mean curvature and shape operator of isometric immersions in real-space-forms},
     journal = {Glasgow mathematical journal},
     pages = {87--97},
     year = {1996},
     volume = {38},
     number = {1},
     doi = {10.1017/S001708950003130X},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708950003130X/}
}
TY  - JOUR
AU  - Chen, Bang-Yen
TI  - Mean curvature and shape operator of isometric immersions in real-space-forms
JO  - Glasgow mathematical journal
PY  - 1996
SP  - 87
EP  - 97
VL  - 38
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S001708950003130X/
DO  - 10.1017/S001708950003130X
ID  - 10_1017_S001708950003130X
ER  - 
%0 Journal Article
%A Chen, Bang-Yen
%T Mean curvature and shape operator of isometric immersions in real-space-forms
%J Glasgow mathematical journal
%D 1996
%P 87-97
%V 38
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S001708950003130X/
%R 10.1017/S001708950003130X
%F 10_1017_S001708950003130X

[1] 1.Chen, B. Y., Geometry of Submanifolds, (Marcel Dekker, New York, 1973). Google Scholar

[2] 2.Chen, B. Y., Some pinching and classification theorems for minimal submanifolds, Archiv der Math. 60 (1993), 568–578. Google Scholar | DOI

[3] 3.Chen, B. Y., A Riemannian invariant for submanifolds in space forms and its applications, Geometry and Topology of Submanifolds (Dillen, F. and Verstraelen, L., eds.), vol. VI, 1994, pp. 58–81. Google Scholar

[4] 4.Chen, B. Y., A Riemannian invariant and its applications to submanifold theory, Results in Math. 27 (1995), 17–26. Google Scholar | DOI

[5] 5.Erbacher, J., Reduction of the codimension of an isometric immersion, J. Differential Geometry 5 (1971), 333–340. Google Scholar | DOI

[6] 6.Leung, P. F., On a relation between the topology and the intrinsic and extrinsic geometries of a compact submanifold, Proc. Edinburgh Math. Soc. 28 (1985), 305–311. Google Scholar | DOI

Cité par Sources :