A dimensional restriction for a class of contact manifolds

• Autorzy: Loiudice E.

Identyfikatory

DOI

10.1515/dema-2017-0021

• Języki publikacji: EN

Abstrakty

EN

In this work we consider a class of contact manifolds (M, η) with an associated almost contact metric structure (φ, ξ, η, g). This class contains, for example, nearly cosymplectic manifolds and the manifolds in the class C9 ⊕ C10 defined by Chinea and Gonzalez. All manifolds in the class considered turn out to have dimension 4n + 1. Under the assumption that the sectional curvature of the horizontal 2-planes is constant at one point, we obtain that these manifolds must have dimension 5.

Słowa kluczowe

EN

almost contact metric structure; contact manifold; Chinea-Gonzalez classification

PL

struktura metryczna; rozmaitość kontaktowa; klasyfikacja Chinea-Gonzaleza

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2017
• Tom: Vol. 50, nr 1
• Strony: 231--238
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Loiudice E.

• Dipartimento di Matematica, Università di Bari Aldo Moro, Via Orabona 4, 70125 Bari, Italy

Bibliografia

• [1] Chern S. S., Pseudo-groupes continus infinis. Colloques Internationaux du C. N. R. S., Strasbourg, 1953, 119-136
• [2] Blair D. E., Riemannian geometry of contact and symplectic manifolds, Progress in Mathematics, Birkhauser Boston, Inc., Boston, MA, second edition, 2010, 203
• [3] Olszak Z., On contact metric manifolds, Tohoku Math. J. (2), 1979, 31(2), 247-253
• [4] Blair D. E., On the non-existence of flat contact metric structures, Tohoku Math. J. (2), 1976, 28(3), 373-379
• [5] Chinea D., Gonzalez C., A classification of almost contact metric manifolds, Ann. Mat. Pura Appl., 1990, 156(1), 15-36
• [6] Endo H., On the curvature tensor of nearly cosymplectic manifolds of constant φ-sectional curvature, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.), 2005, 51, 439-454

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).