Skip to main content Accessibility help
×
Home

Generalized Goldberg Formula

  • Antonio De Nicola (a1) and Ivan Yudin (a1)

Abstract

In this paper we prove a useful formula for the graded commutator of the Hodge codifferential with the left wedge multiplication by a fixed $p$ -form acting on the de Rham algebra of a Riemannian manifold. Our formula generalizes a formula stated by Samuel $\text{I}$ . Goldberg for the case of 1-forms. As first examples of application we obtain new identities on locally conformally Kähler manifolds and quasi-Sasakian manifolds. Moreover, we prove that under suitable conditions a certain subalgebra of differential forms in a compact manifold is quasi-isomorphic as a $\text{CDGA}$ to the full de Rham algebra.

Copyright

References

Hide All
[1] Boyer, C. P. and Galicki, K., Sasakian geometry. Oxford Mathematical Monographs, Oxford University Press, Oxford, 2008.
[2] Cappelletti-Montano, B., De Nicola, A., and Yudin, I., A survey on cosymplectic geometry.Rev. Math.Phys. 25(2013), no. 10, 1343002, 55.http://dx.doi.org/10.1142/S0129055X13430022
[3] Cappelletti-Montano, B., De Nicola, A., and Yudin, I., Hard Lefschetz theorem for Sasakian manifolds. J. Differential Geom. 101(2015), no. 1, 4766.
[4] Deligne, P., Griffiths, P., Morgan, J., and Sullivan, D., Real homotopy theory of Kâhler manifolds. Invent. Math. 29(1975), no. 3, 245274. http://dx.doi.org/10.1007/BF01389853
[5] Dragomir, S. and Ornea, L., Locally conformal Kähler geometry.Progress in Mathematics, 155, Birkhäuser Boston, Inc., Boston, MA, 1998. http://dx.doi.org/10.1007/978-1-4612-2026-8
[6] Frölicher, A. Nijenhuis, A., Theory of vector-valued differential forms. I. Derivations of the graded ring of differential forms. Nederl.Akad.Wetensch.Proc. Ser. A. 59; Indag.Math. 18(1956), 338359. http://dx.doi.org/10.1016/S1385-7258(56)50046-7
[7] Frölicher, A. Nijenhuis, A., Some new cohomology invariants for complex manifolds. I. II. Nederl.Akad.Wetensch. Proc. Ser. A. 59; Indag.Math. 18(1956), 540552, 553-564.
[8] Fujitani, T., Complex-valued differential forms on normal contact Riemannian manifolds. Tôhoku Math. J. (2) 18(1966), 349361. http://dx.doi.org/10.2748/tmjV1178243376
[9] Goldberg, S. I., Conformal transformations of Kaehler. Bull. Amer. Math. Soc. 66(1960), 5458. http://dx.doi.org/10.1090/S0002-9904-1960-10390-4
[10] Goldberg, S. I., Curvature and homology. Pure and Applied Mathematics, 11, Academic Press, New York-London, 1962.
[11] Kanemaki, S., Quasi-Sasakian manifolds. Tôhoku Math. J. 29(1977), no. 2, 227233. http://dx.doi.org/! 0.2748/tmj/11 78240654
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Keywords

Generalized Goldberg Formula

  • Antonio De Nicola (a1) and Ivan Yudin (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed