Abstract
On a real hypersurface in the complex quadric we can consider the Levi-Civita connection and, for any nonnull constant k, the k-th generalized Tanaka-Webster connection. We also have a differential operator of first order of Lie type associated to the k-th generalized Tanaka-Webster connection. We prove non-existence of real hypersurfaces in the complex quadric for which the covariant derivatives associated to both connections coincide or Lie derivative and Lie type differential operator coincide when they act on the shape operator of the real hypersurface.
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Pérez, J.d.D., Suh, Y.J. Derivatives of the Shape Operator of Real Hypersurfaces in the Complex Quadric. Results Math 73, 126 (2018). https://doi.org/10.1007/s00025-018-0888-4
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DOI: https://doi.org/10.1007/s00025-018-0888-4
Keywords
- Complex quadric
- real hypersurface
- shape operator
- k-th generalized Tanaka-Webster connection
- Lie derivative
- Cho operators