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Extensions of flat partial connections

✍ Scribed by Ihor Mykytyuk

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
119 KB
Volume
12
Category
Article
ISSN
0926-2245

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✦ Synopsis

It is proved that any flat partial connection βˆ‡ F on a line bundle L over a manifold M, where F is a complex integrable subbundle of (T M) C , admits an extension to a connection βˆ‡ on L. The kernel of the curvature form Ο‰ of βˆ‡ is investigated. These results are applied to description of the Bohr-Sommerfeld subset in geometric quantization theory and quantization of the motion in the potential Ξ» 2 x 2 + Β΅ 2 /x 2 .

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