A study of the relation between Einstein-Weyl structures and almost contact metric structures
| Project/Area Number |
15540101
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Akita National College of Technology |
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Principal Investigator |
NARITA Fumio Akita National College of Technology, Natural Science, Professor, 自然科学系, 教授 (30042310)
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| Project Period (FY) |
2003 – 2004
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| Project Status |
Completed (Fiscal Year 2004)
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| Budget Amount *help |
¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2004: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2003: ¥500,000 (Direct Cost: ¥500,000)
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| Keywords | Weyl manifold / Weyl submersion / Einstein-Weyl manifold / Canonical variation / Pseudo-Schwarzian / Conformal transformation / ワイル多様体 / ワイルしずめ込み / アインシュタイン・ワイル多様体 / 擬シュバルツテンソル |
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| Research Abstract |
I used an idea of the Weyl submersion for a research of the Einstein-Weyl structure of a Weyl manifold. For a Weyl submersion with Weyl totally geodesic fibers, I obtained a necessary and sufficient condition for a Weyl structure of the total space to admits an Einstein-Weyl structure. By using its result, I investigated the Einstein-Weyl structure of an η-Einstein contact metric manifold. Moreover, I studied Einstein-Weyl structures of a canonical variation of the total space of a Weyl submersion with Weyl totally geodesic fibers.
Next, for a Weyl manifold with a torsion-free affine connection, using the pseudo-Schwarzian tensor I investigated some invariants which do not vary under conformal transformations or Mobius transformations.
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Report
(3 results)
Research Products
(3 results)
