Affiliation:
1. * Departamento de Geometría y Topología and IMAG (Instituto de Matemáticas), Universidad de Granada , Granada , SPAIN
2. ** , Granada , SPAIN
3. *** Kyungpook National University, College of Natural Sciences, Department of Mathematics and Research Institute of Real and Complex Manifolds , Daegu , REPUBLIC OF KOREA
Abstract
ABSTRACT
The almost contact metric structure that we have on a real hypersurface M in the complex quadric Qm
= SO
m+2/SO
m
SO
2 allows us to define, for any nonnull real number k, the k-th generalized Tanaka-Webster connection on M,
∇
^
(
k
)
. Associated to this connection, we have Cho and torsion operators
F
X
(
k
)
and
T
X
(
k
)
, respectively, for any vector field X tangent to M. From them and for any symmetric operator B on M, we can consider two tensor fields of type (1,2) on M that we denote by
B
F
(
k
)
and
B
T
(
k
)
, respectively. We classify real hypersurfaces M in Qm
for which any of those tensors identically vanishes, in the particular case of B being the structure Lie operator Lξ
on M.
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