Para-CR structures on almost paracontact metric manifolds

• Autorzy: Wełyczko J.

Identyfikatory

DOI

10.1515/jaa-2014-0012

• Języki publikacji: EN

Abstrakty

EN

Almost paracontact metric manifolds are the famous examples of almost para-CR manifolds. We find necessary and sufficient conditions for such manifolds to be para-CR. Next we examine these conditions in certain subclasses of almost paracontact metric manifolds. Especially, it is shown that normal almost paracontact metric manifolds are para-CR. We establish necessary and sufficient conditions for paracontact metric manifolds as well as for almost para-cosymplectic manifolds to be para-CR. We find also basic curvature identities for para-CR paracontact metric manifolds and study their consequences. Among others, we prove that any para-CR paracontact metric manifold of constant sectional curvature and of dimension greater than 3 must be para-Sasakian and its curvature equal to -1. The last assertion does not hold in dimension 3. We show that a conformally flat para-Sasakian manifold is of constant sectional curvature equal to -1. New classes of examples of para-CR manifolds are established.

Słowa kluczowe

EN

para-CR manifolds; para-Sasakian manifolds; almost paracontact metric manifolds; paracontact metric manifolds; almost para-cosymplectic manifolds

PL

rozmaitości para-CR; rozmaitości para-Sasakiana; rozmaitości kontaktowe metryczne; rozmaitości parakontaktowe metryczne

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2014
• Tom: Vol. 20, nr 2
• Strony: 105--117
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Wełyczko J.

• Institute of Mathematics and Computer Science, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Bibliografia

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