Author
Basil J. Papantoniou
Bio: Basil J. Papantoniou is an academic researcher from University of Patras. The author has contributed to research in topics: Lie group & Unimodular matrix. The author has an hindex of 1, co-authored 1 publications receiving 314 citations.
Papers
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TL;DR: In this article, a study of contact metric manifolds for which the characteristic vector field of the contact structure satisfies a nullity type condition, condition (*) below, is presented.
Abstract: This paper presents a study of contact metric manifolds for which the characteristic vector field of the contact structure satisfies a nullity type condition, condition (*) below. There are a number of reasons for studying this condition and results concerning it given in the paper: There exist examples in all dimensions; the condition is invariant underD-homothetic deformations; in dimensions>5 the condition determines the curvature completely; and in dimension 3 a complete, classification is given, in particular these include the 3-dimensional unimodular Lie groups with a left invariant metric.
325 citations
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TL;DR: In this paper, generalized Sasakian-space-forms are introduced and studied, by using some different geometric techniques such as Riemannian submersions, warped products or conformal and related transformations.
Abstract: Generalized Sasakian-space-forms are introduced and studied. Many examples of these manifolds are presented, by using some different geometric techniques such as Riemannian submersions, warped products or conformal and related transformations. New results on generalized complex-space-forms are also obtained.
202 citations
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TL;DR: In this article, Boyer and Galicki showed that a complete K-contact gradient soliton is a Jacobi vector field along the geodesics of the Reeb vector field.
Abstract: Inspired by a result of Boyer and Galicki, we prove that a complete K-contact gradient soliton is compact Einstein and Sasakian. For the non-gradient case we show that the soliton vector field is a Jacobi vector field along the geodesics of the Reeb vector field. Next we show that among all complete and simply connected K-contact manifolds only the unit sphere admits a non-Killing holomorphically planar conformal vector field (HPCV). Finally we show that, if a (k, μ)-contact manifold admits a non-zero HPCV, then it is either Sasakian or locally isometric to E3 or En+1 × Sn (4).
157 citations
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17 Jul 2003
TL;DR: In this article, an introductory text on the more topological aspects of contact geometry, written for the Handbook of Differential Geometry vol 2, is presented, along with a detailed exposition of the original proof of the Lutz-Martinet theorem.
Abstract: This is an introductory text on the more topological aspects of contact geometry, written for the Handbook of Differential Geometry vol 2 After discussing (and proving) some of the fundamental results of contact topology (neighbourhood theorems, isotopy extension theorems, approximation theorems), I move on to a detailed exposition of the original proof of the Lutz-Martinet theorem The text ends with a guide to the literature
106 citations
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TL;DR: An up-to-date overview of geometric and topological properties of cosymplectic and coKaehler manifolds is given in this paper, where the authors also mention some of their applications to time-dependent mechanics.
Abstract: We give an up-to-date overview of geometric and topological properties of cosymplectic and coKaehler manifolds. We also mention some of their applications to time-dependent mechanics.
91 citations
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TL;DR: In this paper, contact metric and trans-Sasakian generalized Sasakian-space-forms are deeply studied and general results for manifolds with dimension greater than or equal to 5 are presented.
Abstract: In this paper, contact metric and trans-Sasakian generalized Sasakian-space-forms are deeply studied. We present some general results for manifolds with dimension greater than or equal to 5, and we also pay a special attention to the 3-dimensional cases.
86 citations