JP Journal of Geometry and Topology
Volume 21, Issue 3, Pages 181 - 213
(August 2018) http://dx.doi.org/10.17654/GT021030181 |
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A CONSTRUCTION OF SOLUTIONS TO THE WAVE EQUATION ON THE DE SITTER 4-SPACE VIA TWISTOR METHOD
Tomoyoshi Nakayama
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Abstract: In the context of twistor theory, it is known that there is a one-to-one correspondence between solutions of the wave equation on the three-dimensional de Sitter space and smooth functions satisfying a certain condition on the two-sphere. This correspondence is explicitly described via specific integral transforms. In this paper, we deal with a higher dimensional case, and we establish a correspondence from smooth functions on the three-sphere to solutions of the wave equation on the four-dimensional de Sitter space. This will be of interesting issue from a point of view of mathematical physics, too. |
Keywords and phrases: twistor method, indefinite metric, de Sitter space, wave equation, integral transform. |
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