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EnglishWe prove that any simply connected S-manifold of CR-codimension $s\ge 2$ is noncompact by showing that the complete, simply connected S-manifolds are all the CR products NxR^{s-1} with N Sasakian, endowed with a suitable product metric. N is a Sasakian φ-symmetric space if and only if M is CR-symmetric. The locally CR-symmetric S-manifolds are characterized by $\tilde\nabla\tilde R=0$ where $\tilde\nabla$ is the Tanaka-Webster connection. This characterization is showed to be nonvalid for nonnormal almost S-manifolds.
On the structure and symmetry properties of almost S-manifolds / Dileo G; Lotta A. - In: GEOMETRIAE DEDICATA. - ISSN 0046-5755. - 110:1(2005), pp. 191-211.
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| Titolo: | On the structure and symmetry properties of almost S-manifolds | |
| Autori: | ||
| Data di pubblicazione: | 2005 | |
| Rivista: | ||
| Citazione: | On the structure and symmetry properties of almost S-manifolds / Dileo G; Lotta A. - In: GEOMETRIAE DEDICATA. - ISSN 0046-5755. - 110:1(2005), pp. 191-211. | |
| Abstract: | We prove that any simply connected S-manifold of CR-codimension $s\ge 2$ is noncompact by showing that the complete, simply connected S-manifolds are all the CR products NxR^{s-1} with N Sasakian, endowed with a suitable product metric. N is a Sasakian φ-symmetric space if and only if M is CR-symmetric. The locally CR-symmetric S-manifolds are characterized by $\tilde\nabla\tilde R=0$ where $\tilde\nabla$ is the Tanaka-Webster connection. This characterization is showed to be nonvalid for nonnormal almost S-manifolds. | |
| Handle: | http://hdl.handle.net/11586/126486 | |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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