논문KCI 등재
On deformed-Sasaki metric and harmonicity in tangent bundles
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In this paper, we introduce the deformed-Sasaki metric on the tangent bundle $TM$ over an $m$-dimensional Riemannian manifold $(M, g)$, as a new natural metric on $TM$. We establish a necessary and sufficient conditions under which a vector field is harmonic with respect to the deformed-Sasaki Metric. We also construct some examples of harmonic vector fields.
Abstract
In this paper, we introduce the deformed-Sasaki metric on the tangent bundle $TM$ over an $m$-dimensional Riemannian manifold $(M, g)$, as a new natural metric on $TM$. We establish a necessary and sufficient conditions under which a vector field is harmonic with respect to the deformed-Sasaki Metric. We also construct some examples of harmonic vector fields.
참고문헌 (12)
- M. T. K. Abbassi, "On natural metrics on tangent bundles of Riemannian manifolds", Arch. Math. (Brno), 41(1), pp.71~92 (2005)
- J. Cheeger, "On the structure of complete manifolds of nonnegative curvature", Ann. of Math. (2), 96, pp.413~443 (1972)[DOI]
- M. Djaa, "The geometry of tangent bundles of order r", Boletin Academia, Galega de Ciencias, 4, pp.147~165 (1985)
- P. Dombrowski, "On the geometry of the tangent bundle", J. Reine Angew. Math, 210, pp.73~88 (1962)[DOI]
- J. Eells, "Another report on harmonic maps", Bull. London Math. Soc, 20(5), pp.385~524 (1988)[DOI]
- J. Eells, Jr., "Harmonic mappings of Riemannian manifolds", Amer. J. Math, 86, pp.109~160 (1964)[DOI]
- S. Gudmundsson, "On the geometry of the tangent bundle with the Cheeger-Gromoll metric", Tokyo J. Math, 25(1), pp.75~83 (2002)[DOI]
- F. Latti, "Mus-Sasaki metric and harmonicity", Math. Sci. Appl. E-Notes, 6(1), pp.29~36 (2018)
- A. Salimov, "On the geometry of the (1, 1)-tensor bundle with Sasaki type metric", Chin. Ann. Math. Ser. B, 32(3), pp.369~386 (2011)[DOI]
- S. Sasaki, "On the differential geometry of tangent bundles of Riemannian manifolds. II", Tohoku Math. J. (2), 14, pp.146~155 (1962)[DOI]
- K. Yano, "Tangent and Cotangent Bundles: differential geometry" (1973), Marcel Dekker, Inc
- A. Zagane, "On geodesics of warped Sasaki metric", Math. Sci. Appl. E-Notes, 5(1), pp.85~92 (2017)
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