New Results on Derivatives of the Shape Operator of Real Hypersurfaces in the Complex Quadric

Authors : Juan De Dios Perez, David Pérez-lópez

Pages : 221-231

Doi:10.36890/iejg.1466325

View : 29 | Download : 58

Publication Date : 2024-04-23

Article Type : Research Paper

Abstract :A real hypersurface $M$ in the complex quadric $Q^{m}=SO_{m+2}/SO_mSO_2$ inherits an almost contact metric structure . This structure allows to define, for any nonnull real number $k$, the so called $k$-th generalized Tanaka-Webster connection on $M$, $\\hat{\\nabla}^{(k)}$. If $\\nabla$ denotes the Levi-Civita connection on $M$, we introduce the concepts of $(\\hat{\\nabla}^{(k)},\\nabla)$-Codazzi and $(\\hat{\\nabla}^{(k)},\\nabla)$-Killing shape operator $S$ of the real hypersurface and classify real hypersurfaces in $Q$ satisfying any of these conditions.
Keywords : Complex quadric, real hypersurface, shape operator, k th generalized Tanaka Webster connection, Cho operators