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CR-submanifolds of locally conformal Kaehler manifolds and Riemannian submersions

Fumio Narita (1996)

Colloquium Mathematicae

We consider a Riemannian submersion π: M → N, where M is a CR-submanifold of a locally conformal Kaehler manifold L with the Lee form ω which is strongly non-Kaehler and N is an almost Hermitian manifold. First, we study some geometric structures of N and the relation between the holomorphic sectional curvatures of L and N. Next, we consider the leaves M of the foliation given by ω = 0 and give a necessary and sufficient condition for M to be a Sasakian manifold.

Curvature tensors and Ricci solitons with respect to Zamkovoy connection in anti-invariant submanifolds of trans-Sasakian manifold

Payel Karmakar (2022)

Mathematica Bohemica

The present paper deals with the study of some properties of anti-invariant submanifolds of trans-Sasakian manifold with respect to a new non-metric affine connection called Zamkovoy connection. The nature of Ricci flat, concircularly flat, ξ -projectively flat, M -projectively flat, ξ - M -projectively flat, pseudo projectively flat and ξ -pseudo projectively flat anti-invariant submanifolds of trans-Sasakian manifold admitting Zamkovoy connection are discussed. Moreover, Ricci solitons on Ricci flat,...

Dégénerescence locale des transformations conformes pseudo-riemanniennes

Charles Frances (2012)

Annales de l’institut Fourier

Nous étudions l’ensemble Conf ( M , N ) des immersions conformes entre deux variétés pseudo-riemanniennes ( M , g ) et ( N , h ) . Nous caractérisons notamment l’adhérence de Conf ( M , N ) dans l’espace des applications continues 𝒞 0 ( M , N ) , et décrivons quelques propriétés géométriques de ( M , g ) lorsque cette adhérence est non triviale.

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