The decomposition of almost paracontact metric manifolds in eleven classes revisited
Simeon Zamkovoy,Galia Nakova +1 more
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In this article, the covariant derivative of the structure tensor field is used to define the classes of quasi-para-Sasakian, normal, paracontact metric, para-Sakian and K-parAContact.Abstract:
This paper is a continuation of our previous work, where eleven basic classes of almost paracontact metric manifolds with respect to the covariant derivative of the structure tensor field were obtained. First we decompose one of the eleven classes into two classes and the basic classes of the considered manifolds become twelve. Also, we determine the classes of $$\alpha $$
-para-Sasakian, $$\alpha $$
-para-Kenmotsu, normal, paracontact metric, para-Sasakian, K-paracontact and quasi-para-Sasakian manifolds. Moreover, we study 3-dimensional almost paracontact metric manifolds and show that they belong to four basic classes from the considered classification. We define an almost paracontact metric structure on any 3-dimensional Lie group and give concrete examples of Lie groups belonging to each of the four basic classes, characterized by commutators on the corresponding Lie algebras.read more
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Lie groups as 3-dimensional almost paracontact almost paracomplex Riemannian manifolds
Mancho Manev,Veselina Tavkova +1 more
TL;DR: In this paper, almost paracontact Riemannian manifolds of the lowest dimension 3 were constructed on a family of Lie groups and the obtained manifolds were studied. And the Curvature properties of these manifolds are investigated.
Journal ArticleDOI
Matrix Lie Groups as 3-Dimensional Almost Paracontact Almost Paracomplex Riemannian Manifolds
Mancho Manev,Veselina Tavkova +1 more
TL;DR: In this article, a correspondence between the Lie algebra and the explicit matrix representation of a Lie group is established for Riemannian RiemANNs, where the Lie groups are considered as three-dimensional almost paracontact almost-paracomplex Riemmannian manifolds.
Posted ContentDOI
On Almost Paracontact Almost Paracomplex Riemannian Manifolds
Mancho Manev,Veselina Tavkova +1 more
TL;DR: In this paper, the components of the fundamental (0, 3)-tensor, derived by the covariant derivative of the structure endomorphism and the metric on the considered manifolds in each of the basic classes, are obtained.
Journal ArticleDOI
Statistical submanifolds from a viewpoint of the Euler inequality
Naoto Satoh,Hitoshi Furuhata,Izumi Hasegawa,Toshiyuki Nakane,Yukihiko Okuyama,Kimitake Sato,Mohammad Shahid,Aliya Naaz Siddiqui +7 more
TL;DR: In this article, the Euler inequality for statistical submanifolds is generalized to include doubly autoparallel statistical submansifolds in warped product spaces, for which the equality holds at each point.
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Characterizations of PR-Pseudo-Slant Warped Product Submanifold of Para-Kenmotsu Manifold with Slant Base
TL;DR: In this paper , the authors derived necessary and sufficient conditions for a PR-pseudo-slant submanifold of a para-Kenmotsu manifold to be a warped product.
References
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Book
Riemannian Geometry of Contact and Symplectic Manifolds
TL;DR: In this article, the authors describe a complex geometry model of Symplectic Manifolds with principal S1-bundles and Tangent Sphere Bundles, as well as a negative Xi-sectional Curvature.
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The sixteen classes of almost Hermitian manifolds and their linear invariants
Alfred Gray,Luis Hervella +1 more
TL;DR: In this paper, it was shown that sixteen classes of almost Hermitian manifolds can be found in the Euclidean space, and that they are Hermitians in a natural way.
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Canonical connections on paracontact manifolds
TL;DR: In this article it was shown that an almost paracontact structure admits a connection with totally skew-symmetric torsion if and only if the Nijenhuis tensor of the structure is skew symmetric and the defining vector field is Killing.
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Almost paracontact and parahodge structures on manifolds
Soji Kaneyuki,Floyd L. Williams +1 more
Journal ArticleDOI
On Legendre Curves in 3-Dimensional Normal Almost Paracontact Metric Manifolds
TL;DR: In this article, the curvature and torsion properties of Legendre curves in 3-dimensional normal almost paracontact metric manifolds are studied, and properties of non-Frenet Legendre curve (with null tangents or null normals or null binormals) are obtained.
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The decomposition of almost paracontact metric manifolds in eleven classes revisited
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