The aim of this paper is to investigate n-dimensional real submanifolds of complex manifolds in the case when the maximal holomorphic tangent space is (n-1)-dimensional. In particular, we give some examples and we consider the Levi form on these submanifolds, especially when the ambient space is a complex space form. Moreover, we show that on some remarkable class of real hypersurfaces of complex space forms, the Levi form cannot vanish identically.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc57-0-6,
author = {Mirjana Djori\'c and Masafumi Okumura},
title = {CR submanifolds of maximal CR dimension in complex manifolds},
journal = {Banach Center Publications},
volume = {58},
year = {2002},
pages = {89-99},
zbl = {1038.53055},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc57-0-6}
}
Mirjana Djorić; Masafumi Okumura. CR submanifolds of maximal CR dimension in complex manifolds. Banach Center Publications, Tome 58 (2002) pp. 89-99. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc57-0-6/