| Title:
|
Geometric properties of a sequence of standard minimal immersions between spheres (English) |
| Author:
|
Gasparini, Ida Cattaneo |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
49 |
| Issue:
|
2 |
| Year:
|
1999 |
| Pages:
|
401-414 |
| . |
| Category:
|
math |
| . |
| MSC:
|
53C22 |
| MSC:
|
53C30 |
| MSC:
|
53C42 |
| idZBL:
|
Zbl 0974.53043 |
| idMR:
|
MR1692516 |
| . |
| Date available:
|
2009-09-24T10:23:44Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127496 |
| . |
| Reference:
|
[B] M. Berger, P. Gauduchon, E. Mazet: Le spèctre d’une variètè Riemannienne.Lecture Notes in Math. 194, Springer-Verlag, 1971. MR 0282313 |
| Reference:
|
[Be] A.L. Besse: Manifolds all of whose geodesics are closed.Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 93, Springer-Verlag, 1978. Zbl 0387.53010, MR 0496885 |
| Reference:
|
[C] I. Cattaneo Gasparini: Some remarks on the second variation formula for the area.Annals of Global Analysis and Geometry 11 (1993), 221–235. Zbl 0818.53078, MR 1237455 |
| Reference:
|
[Ca] E. Calabi: Minimal immersions of surfaces in Euclidean spheres.J. Differential Geom. 1 (1967), 111–125. Zbl 0171.20504, MR 0233294, 10.4310/jdg/1214427884 |
| Reference:
|
[Car] A. Carfagna d’Andrea: Immersions with parallel higher fundamental forms.Beiträge zur Algebra und Geometrie 37 (1996), 75–86. MR 1407807 |
| Reference:
|
[C.S] S. Console, A. Sanini: Submanifolds with conformal second fundamental form and isotropic immersions.Rivista di Matematica Univ. Parma (1993). MR 1230604 |
| Reference:
|
[C.dC.K] S.S. Chern, M. do Carmo, S. Kobayashi: On minimal submanifolds of a sphere with second fundamental form of constant length.Funct. Analysis and Related Fields, Springer, New-York, 1970, pp. 59–75. MR 0273546 |
| Reference:
|
[Che] B.Y. Chen: Geometry of Submanifolds.Marcel Decker, 1973. Zbl 0262.53036, MR 0353212 |
| Reference:
|
[C.R] I. Cattaneo Gasparini, G. Romani: Normal and osculating maps for submanifolds of $R^n$.Proc. Roy. Soc. Edinburg, Sect. A 114 (1990), 39–55. MR 1051606, 10.1017/S0308210500024252 |
| Reference:
|
[d-W$_1$] M. do Carmo, N. Wallach: Representation of compact groups and minimal immersions into spheres.J. Differential Geom. 4 (1970), 91–104. MR 0266104, 10.4310/jdg/1214429278 |
| Reference:
|
[d-W$_2$] M. do Carmo, N. Wallach: Minimal immersions of spheres into spheres.Ann. of Math. (2) 93 (1971), 43–62. MR 0278318, 10.2307/1970752 |
| Reference:
|
[De-Z] D. De Turck, W. Ziller: Minimal immersions of spherical space forms in spheres.Comment. Math. Helvetici 67 (1992), 428–438. 10.1007/BF02566512 |
| Reference:
|
[E-R] J. Eells and A. Ratto: Harmonic maps and minimal immersions with symmetries.Ann. of Math. Studies 130 (1993), Princeton Univ. Press. MR 1242555 |
| Reference:
|
[E.S] J. Eells and A. Sampson: Harmonic mappings of Riemannian manifolds.American J. Math. 86 (1964), 109–160. MR 0164306, 10.2307/2373037 |
| Reference:
|
[H] W.Y. Hsiang: On compact homogeneous minimal submanifolds.Proc. Nat. Acad. Sci. USA 56 (1966), 5–6. MR 0205203, 10.1073/pnas.56.1.5 |
| Reference:
|
[K.N] S. Kobayashi and K. Nomizu: Foundations of Differential Geometry, Vol. I and II.Interscience, New York, 1963 and 1969. MR 0152974 |
| Reference:
|
[K] O. Kowalski: Generalized symmetric spaces.Lecture Notes in Math. 805, Springer-Verlag, 1980. Zbl 0431.53042, MR 0579184 |
| Reference:
|
[L] H.B. Lawson Jr.: Lectures on minimal submanifolds, Vol I..Publish or Perisch, Univ. of California, Berkeley, 1980. Zbl 0434.53006, MR 0576752 |
| Reference:
|
[Li] A. Lichnerowicz: Gèomètrie des groupes de transformations.Dunod, Paris, 1958. Zbl 0096.16001, MR 0124009 |
| Reference:
|
[Sa] K. Sakamoto: Helical immersions into unit sphere.Math. Ann. 261 (1982), 63–80. MR 0675208, 10.1007/BF01456411 |
| Reference:
|
[Si] J. Simons: Minimal varieties in Riemannian manifolds.Ann. of Math. 88 (1968), 62–105. Zbl 0181.49702, MR 0233295, 10.2307/1970556 |
| Reference:
|
[Sp.] M. Spivak: A comprehensive introduction to differential geometry.Publish or Perish, (1979). Zbl 0439.53005 |
| Reference:
|
[T] T. Takahashi: Minimal immersion of Riemannian manifolds.J. Math. Soc. Japan 18 (1966), 380–385. MR 0198393, 10.2969/jmsj/01840380 |
| Reference:
|
[Th] G. Thorbergsson: Isoparametric submanifold and their buildings.Ann. Math. 133 (1991), 493–498. MR 1097244 |
| Reference:
|
[To] G. Toth: Harmonic and Minimal Maps with Applications in Geometry and Physics.Ellis Horwood Series, 1984. Zbl 0545.58003, MR 0770205 |
| Reference:
|
[Ts] K. Tsukada: Isotropic minimal immersions of spheres into spheres.J. Math. Soc. Japan 35 (1983), 355–379. Zbl 0583.53050, MR 0692333, 10.2969/jmsj/03520355 |
| Reference:
|
[V] N. Vilenkin: Special Functions and the Theory of Groups Representation.Transl. Math. Monograph, Vol. 22, American Math. Soc. Providence, 1968. MR 0229863 |
| Reference:
|
[Vi] J. Vilms: Totally geodesic maps.J. Diff. Geom. 4 (1970), 73–79. Zbl 0194.52901, MR 0262984, 10.4310/jdg/1214429276 |
| Reference:
|
[W,H] T.J. Willmore and N. Hitchin: Global Riemannian Geometry.Ellis Horwood Series, 1989. |
| . |
