Abstract
In this article, we first study the generalised notion of parallel Jacobi operator known as recurrent Jacobi operator in complex quadric \(Q^{m} = SO_{m+2}/SO_{m}SO_{2}\). Using this generalised notion, we describe recurrent normal Jacobi operator and recurrent structure Jacobi operator in complex quadric \(Q^{m}\) and we investigate Hopf real hypersurfaces of complex quadric \(Q^{m}\) with recurrent normal Jacobi operator and recurrent structure Jacobi operator. Consequently, we prove the non-existence results with these geometric conditions.
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Suh, Y.J.: Real hypersurfaces in the complex quadric with parallel normal Jacobi operator. Math. Nachr. 290(2–3), 442–451 (2017)
Jeong, I., Pérez, J.D., Suh, Y.J.: Recurrent Jacobi Operator of real hypersurfaces in complex two-plane Grassmannians. Bull. Korean Math. Soc. 50(2), 525-536 (2013)
Smyth, B.: Differential geometry of complex hypersurfaces. Ann. Math. 85, 246–266 (1967)
Reckziegel,H.: On the geometry of the complex quadric. In: Geometry and Topology of Submanifolds VIII, pp. 302–315. World Scientific Publishing, Brussels/Nordfjordeid, River Edge, NJ (1995)
Berndt, J., Suh, Y.J.: Contact hypersurfaces in K\(\ddot{a}\)hler manifold. Proc. Amer. Math. Soc. 23, 2637–2649 (2015)
Klein, S.: Totally geodesic submanifolds in the complex quadric. Differential Geom. Appl. 26, 79–96 (2008)
Suh, Y.J.: Real hypersurfaces in the complex quadric with Reeb parallel shape operator. Int. J. Math. 25, 1450059, 17 pp. (2014)
Blair, D. E.: Contact Manifolds in Riemannian Geometry. Lecture Notes in Mathematics, vol. 509. Springer, Berlin (1976)
Berndt, J., Suh, Y.J.: Real hypersurfaces with isometric Reeb flow in complex quadrics. Int. J. Math. 24, 1350050, 18 pp. (2013)
Perez, J.D., Santos, F.G.: Real hypersurfaces in complex projective space with recurrent structure Jacobi operator. Diff. Geom. Appl. 26, 218–223 (2008)
Pérez,J.D., Santos,F.G., Suh,Y. J.: Real hypersurfaces in complex projective space whose structure Jacobi operator is \(D\)-parallel. Bull. Belgian Math. Soc. Simon Stevan 13, 459-469 (2006)
Bansal, P., Shahid, M.H.: Optimization Approach for Bounds Involving Generalized Normalized \(\delta \)-Casorati Curvatures, Accepted in AISC series, Springer, (2018)
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Bansal, P. (2019). Hopf Real Hypersurfaces in the Complex Quadric \(Q^{m}\) with Recurrent Jacobi Operator. In: Bansal, J., Das, K., Nagar, A., Deep, K., Ojha, A. (eds) Soft Computing for Problem Solving. Advances in Intelligent Systems and Computing, vol 816. Springer, Singapore. https://doi.org/10.1007/978-981-13-1592-3_57
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DOI: https://doi.org/10.1007/978-981-13-1592-3_57
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