Differential geometry of Cartan domains of type four

Chiara De Fabritiis

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1990)

  • Volume: 1, Issue: 2, page 131-138
  • ISSN: 1120-6330

Abstract

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In this note we compute the sectional curvature for the Bergman metric of the Cartan domain of type IV and we give a classification of complex totally geodesic manifolds for this metric.

How to cite

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De Fabritiis, Chiara. "Differential geometry of Cartan domains of type four." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 1.2 (1990): 131-138. <http://eudml.org/doc/244142>.

@article{DeFabritiis1990,
abstract = {In this note we compute the sectional curvature for the Bergman metric of the Cartan domain of type IV and we give a classification of complex totally geodesic manifolds for this metric.},
author = {De Fabritiis, Chiara},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Curvature; Geodesic; Totally geodesic manifold; Cartan domain; bounded symmetric domain; Bergman kernel function; totally geodesic complex submanifolds},
language = {eng},
month = {5},
number = {2},
pages = {131-138},
publisher = {Accademia Nazionale dei Lincei},
title = {Differential geometry of Cartan domains of type four},
url = {http://eudml.org/doc/244142},
volume = {1},
year = {1990},
}

TY - JOUR
AU - De Fabritiis, Chiara
TI - Differential geometry of Cartan domains of type four
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1990/5//
PB - Accademia Nazionale dei Lincei
VL - 1
IS - 2
SP - 131
EP - 138
AB - In this note we compute the sectional curvature for the Bergman metric of the Cartan domain of type IV and we give a classification of complex totally geodesic manifolds for this metric.
LA - eng
KW - Curvature; Geodesic; Totally geodesic manifold; Cartan domain; bounded symmetric domain; Bergman kernel function; totally geodesic complex submanifolds
UR - http://eudml.org/doc/244142
ER -

References

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  1. ABATE, M., Complex geodesies in classical domains. Scuola Norm. Sup., Pisa1985. 
  2. FRANZONI, T. - VESENTINI, E., Holomorphic maps and invariant distances. North-Holland, Amsterdam1980. Zbl0447.46040MR563329
  3. GENTILI, G., Invariant Riemannian geometry on convex cones. Tesi di perfezionamento, Scuola Norm. Sup., Pisa1981. 
  4. HARRIS, L. A., Bounded symmetric homogeneous domains in infinite dimensional holomorphy. Proceedings on infinite dimensional holomorphy. Springer Verlag, Lect. Notes in Math., 346, 1973, 13-40. Zbl0293.46049MR407330
  5. HIRZEBRUCH, H., Halbraume und ihre holomorphische Automorphismen. Math. Ann., 153, 1964, 395-417. Zbl0124.29303MR159035
  6. HUA, L. K., Harmonic analysis of functions of several variables in the classical domains. Transl. of Am. Math. Soc., R.I., 1963. Zbl0507.32025MR171936
  7. KOBAYASHI, S., Hyperbolic manifolds and holomorphic mappings. Dekker, New York1970. Zbl0207.37902MR277770
  8. KÒCKER, M., Die Geodâtischen von Positivitâtsbereichen. Math. Ann., 135, 1958, 192-202. MR103987
  9. REIFFEN, H., Die Carathéodorysche Distanz und ihre zugehorige Differentialmetrik. Math. Ann., 161, 1965, 315-324. Zbl0141.08803MR196133
  10. ROYDEN, H. L., Complex Finsler metrics. Contemp. Math., 49, 1986, 119-124. Zbl0587.53029MR833808DOI10.1090/conm/049/833808

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