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Commuting Conditions of the k-th Cho operator with the structure Jacobi operator of real hypersurfaces in complex space forms

Konstantina Panagiotidou, Juan de Dios Pérez (2015)

Open Mathematics

In this paper three dimensional real hypersurfaces in non-flat complex space forms whose k-th Cho operator with respect to the structure vector field ξ commutes with the structure Jacobi operator are classified. Furthermore, it is proved that the only three dimensional real hypersurfaces in non-flat complex space forms, whose k-th Cho operator with respect to any vector field X orthogonal to structure vector field commutes with the structure Jacobi operator, are the ruled ones. Finally, results...

Complete Riemannian manifolds admitting a pair of Einstein-Weyl structures

Amalendu Ghosh (2016)

Mathematica Bohemica

We prove that a connected Riemannian manifold admitting a pair of non-trivial Einstein-Weyl structures ( g , ± ω ) with constant scalar curvature is either Einstein, or the dual field of ω is Killing. Next, let ( M n , g ) be a complete and connected Riemannian manifold of dimension at least 3 admitting a pair of Einstein-Weyl structures ( g , ± ω ) . Then the Einstein-Weyl vector field E (dual to the 1 -form ω ) generates an infinitesimal harmonic transformation if and only if E is Killing.

Complex structures on S O g M

Tommaso Pacini (1999)

Bollettino dell'Unione Matematica Italiana

Data una varietà Riemanniana orientata M , g , il fibrato principale S O g M di basi ortonormali positive su M , g ha una parallelizzazione canonica dipendente dalla connessione di Levi-Civita. Questo fatto suggerisce la definizione di una classe molto naturale di strutture quasi-complesse su M , g . Dopo le necessarie definizioni, discutiamo qui l'integrabilità di queste strutture, esprimendola in termini della struttura Riemanniana g .

Conformal and related changes of metric on the product of two almost contact metric manifolds.

David E. Blair, José Antonio Oubiña (1990)

Publicacions Matemàtiques

This paper studies conformal and related changes of the product metric on the product of two almost contact metric manifolds. It is shown that if one factor is Sasakian, the other is not, but that locally the second factor is of the type studied by Kenmotsu. The results are more general and given in terms of trans-Sasakian, α-Sasakian and β-Kenmotsu structures.

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