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Invariant vector fields on contact metric manifolds under \(\mathcal{D}\)-homothetic deformation. (English) Zbl 1484.53112

Summary: In this paper, we study some vector fields on a contact metric manifold which are invariant under a \(\mathcal{D} \)-homothetic deformation.

MSC:

53D10 Contact manifolds (general theory)
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
53C24 Rigidity results
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[1] D. E. Blair, <i>Riemannian geometry of contact and symplectic manifolds</i>, Progress in Mathematics, Birkhauser, Basel, 2010. · Zbl 1246.53001
[2] D, Contact metric manifolds satisfying a nullity condition, Israel J. Math., 91, 189-214 (1995) · Zbl 0837.53038
[3] E. Boeckx, <i>A full classification of contact metric</i> (<i>k, μ</i>)-<i>spaces</i>, Illinois J. Math., 44 (2008), 212-219. · Zbl 0969.53019
[4] E, D-homothetic transforms of φ-symmetric spaces, Mediterr. J. Math., 11, 745-753 (2014) · Zbl 1300.53017
[5] H, On an extended contact Bochner curvature tensor on contact metric manifolds, Colloq. Math., 65, 33-41 (1993) · Zbl 0820.53041
[6] N. H. Gangadharappa, R. Sharma, <i>D-homothetically deformed K-contact Ricci almost solitons</i>, Results Math., 75, (2020), 1-8. · Zbl 1447.53068
[7] A, Holomorphically planar conformal vector fields on contact metric manifolds, Acta Math. Hungar., 129, 357-367 (2010) · Zbl 1240.53057
[8] A. Ghosh, R. Sharma, <i>A generalization of K-contact and</i> (<i>k, μ</i>)-<i>contact manifolds</i>, J. Geom., 103 (2012), 431-443. · Zbl 1262.53026
[9] \(I, \varphi \)(<i>Ric</i>)-vector fields in Riemannian spaces, Arch. Math. (Brno), 44, 385-390 (2008) · Zbl 1212.53018
[10] U, On a class of almost contact metric manifolds, JP J. Geom. Topol., 8, 185-201 (2008) · Zbl 1163.53019
[11] T, Contact strongly pseudo-convex integrable CR metrics as critical points, J. Geom., 59, 94-102 (1997) · Zbl 0880.53027
[12] H, <i>D</i><sub><i>a</i></sub>-homothetic deformation of K-contact manifolds, ISRN Geom., 2013, 392608 (2013) · Zbl 1290.53073
[13] R. Sharma, <i>Certain results on K-contact and</i> (<i>k, μ</i>)-<i>contact manifolds</i>, J. Geom., 89 (2008), 138- 147. · Zbl 1175.53060
[14] R, Conformal and projective characterizations of an odd dimensional unit sphere, Kodai Math. J., 42, 160-169 (2019) · Zbl 1418.53056
[15] R. Sharma, L. Vrancken, <i>Conformal classification of</i> (<i>k, μ</i>)-<i>contact manifolds</i>, Kodai Math. J., 33 (2010), 267-282. · Zbl 1194.53041
[16] S, Note on infinitesimal transformations over contact manifolds, Tohoku Math. J., 14, 416-430 (1962) · Zbl 0112.13903
[17] S, The topology of contact Riemannian manifolds, Illinois J. Math., 12, 700-717 (1968) · Zbl 0165.24703
[18] K. Yano, M. Kon, <i>Structures on manifolds</i>, World Scientific, Singapore, 1984. · Zbl 0557.53001
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