On normal globally framed $f$-manifolds

Goldberg, Samuel I.; Yano, Kentarô

doi:10.2748/tmj/1178242763

Cited by 92 publications

(78 citation statements)

References 4 publications

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“…For these reasons, we consider that it is interesting to introduce a notion of generalized S-space-form on metric f -manifolds (see Section 2 for a precise definition of these manifolds) and we have limited our research to the case s = 2 which appeared in the study of hypersurfaces in almost contact manifolds [3,8]. To this end, we have followed the same procedure as in almost complex and almost contact cases, that is, we have substituted the constants in the expression of the curvature tensor field of an S-space-form (an S-manifold of constant f -sectional curvature) obtained in [10] by certain differentiable functions on the manifold.…”

Section: R(x Y )Z = λ{G(x Z)y − G(y Z)x}mentioning

confidence: 99%

Generalized S-space-forms with two structure vector fields

Carriazo

Fernández

Fuentes

2009

Advg

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Section: R(x Y )Z = λ{G(x Z)y − G(y Z)x}mentioning

confidence: 99%

Generalized S-space-forms with two structure vector fields

Carriazo

Fernández

Fuentes

2009

Advg

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“…A framed metric /-manifold is said to be covariant constant if a number of tensors including/are parallel. As a corollary of Proposition 4.6 we strengthen slightly Theorem 14 of [6]. Corollary 4.7.…”

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confidence: 51%

“…In [6] the authors consider the concept of a framed metric /-manifold which among other things is a Riemannian manifold Af together with a skew-symmetric tensor/of type (1,1) satisfying/3 + / = 0. A framed metric /-manifold is said to be covariant constant if a number of tensors including/are parallel.…”

mentioning

confidence: 99%

Codazzi Tensors and Reducible Submanifolds

Bivens¹

1981

Transactions of the American Mathematical Society

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Abstract. An integral formula is derived for Codazzi tensors of type (k, k). Many of the classical Minkowski type integral formulas then become special cases of this one. If M is a submanifold of Euclidean space and it is a parallel distribution on M then each leaf of m is a submanifold of Euclidean space with mean curvature normal vector field tj. Using the above integral formula we show that the integral of |tj|2 over M is bounded below by an intrinsic constant and we give necessary and sufficient conditions for equality to hold. The reducible surfaces for which equality holds are characterized and related results concerned with Riemannian product manifolds are proved.Parallel tensors of type (1,1) are characterized in terms of the de Rham decomposition. It is shown that if M is irreducible and A is a parallel tensor of type (1, 1) on M which is not multiplication by a constant then M is a Kaehler manifold. Some further results are derived for manifolds whose simply connected cover is Kaehler.

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“…The reader can find more details about these structures in the Riemannian case, for example in [7,8,21] and in [17], where the notion of almost S -manifolds was introduced, while one can principally find in [10] the extension of this theory to the semi-Riemannian context.…”

Section: Preliminariesmentioning

confidence: 99%

Osserman lightlike hypersurfaces of indefinite $\mathcal S$-manifolds

Brunetti¹

2014

Turk J Math

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We mainly deal with the problem of admissibility for screen distributions on a lightlike hypersurface of both a semi-Riemannian manifold and an indefinite S -manifold. In the latter case, we first show that a characteristic screen distribution is never admissible, and then we provide a characterization for admissible screen distributions on proper totally umbilical lightlike hypersurfaces. Finally, in studying Osserman conditions, we characterize Osserman totally umbilical hypersurfaces of a semi-Riemannian manifold, obtaining explicit results on the eigenvalues of the pseudo-Jacobi operators in the case of lightlike hypersurfaces with Lorentzian screen leaves.

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On normal globally framed $f$-manifolds

Cited by 92 publications

References 4 publications

Generalized S-space-forms with two structure vector fields

Generalized S-space-forms with two structure vector fields

Codazzi Tensors and Reducible Submanifolds

Osserman lightlike hypersurfaces of indefinite $\mathcal S$-manifolds

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