A note on the Laplace operator for holomorphic functions on complex Lie groups
DOI:
https://doi.org/10.24193/subbmath.2017.0002Keywords:
Complex Lie group, holomorphic function, Laplace operator, last multiplier.Abstract
In this note we obtain the local expression of the Laplace operator acting on holomorphic functions defined on a complex Lie group. Also, some applications to the theory of holomorphic last multipliers are given.
Mathematics Subject Classification (2010): 22E10, 32M05, 53B20, 53B21, 53C56, 34A26.
References
Goldberg, S.I., Curvature and Homology, Revised Edition, Dover Publication, Inc. Mineola, New-York, 1998.
Crˆa¸sm˘areanu, M., Last multipliers theory on manifolds, Tensor, 66(2005), no. 1, 18–25. [3] Crˆa¸sm˘areanu, M., Last multipliers as autonomous solutions of the Liouville equation of transport, Houston J. Math., 34(2008), no. 2, 455–466.
Crˆa¸sm˘areanu, M., Last multipliers for multivectors with applications to Poisson geometry, Taiwanese J. Math., 13(2009), no. 5, 1623–1636.
Crˆa¸sm˘areanu, M., Last multipliers on weighted manifolds and the weighted Liouville equation, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys., 77 (2015), no. 3 (in press).
Crˆa¸sm˘areanu, M., Ida, C., Popescu, P., Holomorphic last multipliers on complex manifolds, Preprint available to arXiv:submit/1295734 [math.DG] 4 July 2015.
Ida, C., Ionescu, A., On a metric holomorphic connection in complex Lie groups, BSG Proceedings, 21(2014).
Ionescu, A., On lifts of left-invariant holomorphic vector fields on complex Lie groups, Bulletin of Transilvania University, Series III, 7(2014), no. 2.
Kobayashi, S., Nomizu, K., Foundations of Differential Geometry II, Wiley Interscience, New-York, 1969.
LeBrun, C. R., H-Space with a cosmological constant, Proc. R. Soc. Lond. A, 380(1982), 171-185.
Lee, D. H., The structure of complex Lie groups, Research Notes in Mathematics Series, Chapman and Hall/CRC, 232 pag.
Toth, A., Varolin, D., Holomorphic diffeomorphisms of complex semisimple Lie groups, Inventiones Mathematicae, 139(2000), 351–369.
Rund, H., Local differential-geometric structures on Lie groups, Tensor, N.S., 48(1998), 64–87.
Wang, H.-C., Complex Parallelisable Manifolds, Proceedings of the American Math. Soc., 5(1954), no. 5, 71–776.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2017 Studia Universitatis Babeș-Bolyai Mathematica
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
