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REAL HYPERSURFACES OF NON-FLAT COMPLEX SPACE FORMS WITH GENERALIZED ξ-PARALLEL JACOBI STRUCTURE OPERATOR

Part of: Global differential geometry Symplectic geometry, contact geometry

Published online by Cambridge University Press:  23 July 2015

TH. THEOFANIDIS
TH. THEOFANIDIS*
Affiliation:
Department of Civil Engineering, School of Technology, Aristotle University of Thessaloniki, Thessaloniki, 54124, Greece e-mail: onslaught5000@hotmail.com, theotheo@civil.auth.gr
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Abstract

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The aim of the present paper is the classification of real hypersurfaces M equipped with the condition Al = lA, l = R(., ξ)ξ, restricted in a subspace of the tangent space TpM of M at a point p. This class is large and difficult to classify, therefore a second condition is imposed: (∇ξl)X = ω(X)ξ + ψ(X)lX, where ω(X), ψ(X) are 1-forms. The last condition is studied for the first time and is much weaker than ∇ξl = 0 which has been studied so far. The Jacobi Structure Operator satisfying this weaker condition can be called generalized ξ-parallel Jacobi Structure Operator.

MSC classification

Primary: 53C40: Global submanifolds
Secondary: 53D15: Almost contact and almost symplectic manifolds
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 58 , Issue 3 , September 2016 , pp. 677 - 687
Copyright
Copyright © Glasgow Mathematical Journal Trust 2015 

References

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