A certain tensor on real hypersurfaces in a nonflat complex space form

Kazuhiro Okumura

Czechoslovak Mathematical Journal (2020)

• Volume: 70, Issue: 4, page 1059-1077
• ISSN: 0011-4642

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In a nonflat complex space form (namely, a complex projective space or a complex hyperbolic space), real hypersurfaces admit an almost contact metric structure $(\phi ,\xi ,\eta ,g)$ induced from the ambient space. As a matter of course, many geometers have investigated real hypersurfaces in a nonflat complex space form from the viewpoint of almost contact metric geometry. On the other hand, it is known that the tensor field $h$$(=\frac{1}{2}{ℒ}_{\xi }\phi )$ plays an important role in contact Riemannian geometry. In this paper, we investigate real hypersurfaces in a nonflat complex space form from the viewpoint of the parallelism of the tensor field $h$.

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Okumura, Kazuhiro. "A certain tensor on real hypersurfaces in a nonflat complex space form." Czechoslovak Mathematical Journal 70.4 (2020): 1059-1077. <http://eudml.org/doc/296972>.

@article{Okumura2020,
abstract = {In a nonflat complex space form (namely, a complex projective space or a complex hyperbolic space), real hypersurfaces admit an almost contact metric structure $(\phi , \xi , \eta , g)$ induced from the ambient space. As a matter of course, many geometers have investigated real hypersurfaces in a nonflat complex space form from the viewpoint of almost contact metric geometry. On the other hand, it is known that the tensor field $h$$(=\frac\{1\}\{2\} \mathcal \{L\}_\xi \phi )$ plays an important role in contact Riemannian geometry. In this paper, we investigate real hypersurfaces in a nonflat complex space form from the viewpoint of the parallelism of the tensor field $h$.},
author = {Okumura, Kazuhiro},
journal = {Czechoslovak Mathematical Journal},
keywords = {nonflat complex space form; real hypersurface; Hopf hypersurface; ruled real hypersurface; the tensor field $h$},
language = {eng},
number = {4},
pages = {1059-1077},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A certain tensor on real hypersurfaces in a nonflat complex space form},
url = {http://eudml.org/doc/296972},
volume = {70},
year = {2020},
}

TY - JOUR
AU - Okumura, Kazuhiro
TI - A certain tensor on real hypersurfaces in a nonflat complex space form
JO - Czechoslovak Mathematical Journal
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 70
IS - 4
SP - 1059
EP - 1077
AB - In a nonflat complex space form (namely, a complex projective space or a complex hyperbolic space), real hypersurfaces admit an almost contact metric structure $(\phi , \xi , \eta , g)$ induced from the ambient space. As a matter of course, many geometers have investigated real hypersurfaces in a nonflat complex space form from the viewpoint of almost contact metric geometry. On the other hand, it is known that the tensor field $h$$(=\frac{1}{2} \mathcal {L}_\xi \phi )$ plays an important role in contact Riemannian geometry. In this paper, we investigate real hypersurfaces in a nonflat complex space form from the viewpoint of the parallelism of the tensor field $h$.
LA - eng
KW - nonflat complex space form; real hypersurface; Hopf hypersurface; ruled real hypersurface; the tensor field $h$
UR - http://eudml.org/doc/296972
ER -

References

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