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Sollevamenti sul fibrato dei riferimenti di una varietà differenziabile e pseudoconnessioni lineari
No full textCurvature of Locally Conformal Cosymplectic Manifolds
No full textLocally conformal cosymplectic manifolds are investigated from the point of view of the curvature. Particular attention to the N(k)-nullity condition is given and classification theorems in dimension 2n+1>=5 are stated. This also allows
to classify locally conformal cosymplectic manifolds which are locally symmetric spaces
A class of almost contact metric manifolds with pointwise constant phi-sectional curvature
No full textA class of almost contact metric manifolds and double-twisted products
No full textWe determine the Chinea-Gonzales class of almost contact metric manifolds locally realized as double-twisted product manifolds of an open interval and an almost Hermitian manifold, by means of two smooth positive functions. We also give an explicit expression for the cosymplectic defect of any manifold in the considered class and derive several consequences in dimensions 2n+1>3. Explicit formulas for two algebraic curvature tensor fields are obtained. In particular cases, this allows to state interesting curvature relations
Locally conformal C6-manifolds and generalized Sasakian-space-forms
No full textAn algebraic characterization of generalized Sasakian-space-forms is stated. Then, one studies the almost contact metric manifolds which are locally conformal to -manifolds, simply called l.c. -manifolds. In dimension 2n+1>=5, any of these manifolds turns out to
be locally conformal cosymplectic or globally conformal to a Sasakian
manifold. Curvature properties of l.c. -manifolds are obtained, with particular attention to the k-nullity condition. This allows one to state a local classification theorem, in dimension 2n+1>=5, under the hypothesis of constant sectional curvature. Moreover, one proves that an l.c. -manifold is a generalized Sasakian-space-form if and only if it satisfies the k-nullity condition and has pointwise constant -sectional curvature.
Finally, local classification theorems for the generalized Sasakian-space-forms
in the considered class are obtained
A class of almost contact metric manifolds and twisted products
No full textIn the framework of Chinea-Gonzales, we study the class of almost contact metric manifolds locally realized as twisted product manifolds of an open interval and an almost Hermitian manifold, by means of a smooth positive function. Local classification theorems for the generalized Sasakian space-forms in the considered class are obtained, also
Some classes of almost contact metric manifolds and contact Riemannian submersions
No full textLocally conformal almost quasi-Sasakian manifolds are related to the Chinea–Gonzales classification of almost contact metric manifolds. It follows that these manifolds set up a wide class of almost contact metric manifolds containing
several interesting subclasses. Contact Riemannian submersions whose
total space belongs to each of the considered classes are then investigated. The
explicit expression of the integrability tensor and of the mean curvature vector
field of each fibre are given. This allows us to state the integrability of the horizontal
distribution and/or the minimality of the fibres in particular cases. The
classes of the base space and of the fibres are also determined, so extending several well-known results
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