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Abstract
金沢大学人間社会研究域学校教育系 / Institute of Human and Social science, Teacher Education
We introduce a quaternionic invariant for an inclusive immersion into a quaternionic manifold, which is a quaternionic object corresponding to the Willmore functional. The lower bound of this invariant is given by topological invariant and the equality case can be characterized in terms of the natural twistor lift. When the ambient manifold is the quaternionic projective space and the natural twistor lift is holomorphic, we obtain a relation between the quaternionic invariant and the degree of the image of the natural twistor lift as an algebraic curve. Moreover the first variation formula for the invariant is obtained. As an application of the formula, if the natural twistor lift is a harmonic section, then the surface is a stationary point under any variations such that the induced complex structures do not vary. © 2017, Springer-Verlag Berlin Heidelberg.
Embargo Period 12 months
Journal
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- Manuscripta Mathematica
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Manuscripta Mathematica 154 (3-4), 527-549, 2017-11-01
Springer Verlag
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Details 詳細情報について
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- CRID
- 1390290700177166720
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- NII Article ID
- 120006764684
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- NII Book ID
- AA00721187
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- ISSN
- 00252611
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- Web Site
- http://hdl.handle.net/2297/00056038
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- Text Lang
- en
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- Data Source
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- JaLC
- IRDB
- CiNii Articles