The total curvatures of the submanifolds immersed in the Euclidean space have been studied mainly by Santaló and Chern-Kuiper. In this paper we give geometrical and topological interpretation of the total (non absolute) curvatures of the even dimensional submanifolds immersed in Rn+2. This gives a generalization of two results obtained by Santaló.
@article{urn:eudml:doc:44067,
title = {On the total (non absolute) curvature of a even dimensional submanifold Xn immersed in Rn+2.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {7},
year = {1994},
pages = {279-287},
zbl = {0819.53004},
mrnumber = {MR1297515},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44067}
}
Naveira, A. M. On the total (non absolute) curvature of a even dimensional submanifold Xn immersed in Rn+2.. Revista Matemática de la Universidad Complutense de Madrid, Tome 7 (1994) pp. 279-287. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44067/