| Title:
|
On local isometric immersions into complex and quaternionic projective spaces (English) |
| Author:
|
Rivertz, Hans Jakob |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
47 |
| Issue:
|
4 |
| Year:
|
2011 |
| Pages:
|
251-256 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We will prove that if an open subset of $\mathbb{C}{}P^{n}$ is isometrically immersed into $\mathbb{C}{}P^{m}$, with $m<(4/3)n-2/3$, then the image is totally geodesic. We will also prove that if an open subset of $\mathbb{H}{}P^{n}$ isometrically immersed into $\mathbb{H}{}P^{m}$, with $m<(4/3)n-5/6$, then the image is totally geodesic. (English) |
| Keyword:
|
submanifolds |
| Keyword:
|
homogeneous spaces |
| Keyword:
|
symmetric spaces |
| MSC:
|
53C40 |
| idZBL:
|
Zbl 1249.53079 |
| idMR:
|
MR2876947 |
| . |
| Date available:
|
2011-12-16T15:12:20Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141773 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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[9] Rivertz, H. J.: On isometric and conformal immersions into Riemannian spaces.Ph.D. thesis, Department of Mathematics, University of Oslo, 1999. |
| Reference:
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[10] Tomter, P.: Isometric immersions into complex projective space.Lie groups, geometric structures and differential equations—one hundred years after Sophus Lie, vol. 37, Adv. Stud. Pure Math., 2002, pp. 367–396. Zbl 1043.53047, MR 1980909 |
| Reference:
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| . |
