An algebraic characterization of generalized Sasakian-space-forms is stated. Then, one studies the almost contact metric manifolds which are locally conformal to $C_6$-manifolds, simply called l.c. $C_6$-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. $C_6$-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. $C_6$-manifold is a generalized Sasakian-space-form if and only if it satisfies the k-nullity condition and has pointwise constant $\varphi$-sectional curvature. Finally, local classification theorems for the generalized Sasakian-space-forms in the considered class are obtained.
Locally conformal C6-manifolds and generalized Sasakian-space-forms
FALCITELLI, Maria
2010-01-01
Abstract
An algebraic characterization of generalized Sasakian-space-forms is stated. Then, one studies the almost contact metric manifolds which are locally conformal to $C_6$-manifolds, simply called l.c. $C_6$-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. $C_6$-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. $C_6$-manifold is a generalized Sasakian-space-form if and only if it satisfies the k-nullity condition and has pointwise constant $\varphi$-sectional curvature. Finally, local classification theorems for the generalized Sasakian-space-forms in the considered class are obtained.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
