Access the full text.
Sign up today, get DeepDyve free for 14 days.
H. Nakagawa, Ryoichi Takagi (1976)
On locally symmetric Kaehler submanifolds in a complex projective spaceJournal of The Mathematical Society of Japan, 28
E. Calabi (1953)
ISOMETRIC IMBEDDING OF COMPLEX MANIFOLDSAnnals of Mathematics, 58
S. Nakano (1955)
On complex analytic vector bundlesJournal of The Mathematical Society of Japan, 7
W. Bertram (2001)
The Geometry of Jordan and Lie Structures
V. Guillemin, S. Sternberg (1984)
Symplectic Techniques in Physics
N. Mok (1986)
Metric rigidity theorems on Hermitian locally symmetric spaces.Proceedings of the National Academy of Sciences of the United States of America, 83 8
A. Borel (1960)
On the Curvature Tensor of the Hermitian Symmetric ManifoldsAnnals of Mathematics, 71
about characteristic varieties. Furthermore, these orbits can also be described by using the Jordan Algebra approach to Hermitian symmetric spaces, namely, in terms of the so called tripotents
(1992)
Normal holonomy groups and s-representations, Indiana Univ
(2003)
Submanifolds and holonomy, Research
E. Heintze, C. Olmos (1992)
Normal holonomy groups and s-representationsIndiana Univ. Math. J., 41
We wish to thank Carlos Olmos for his many valuable suggestions
C. Olmos (1994)
Homogeneous submanifolds of higher rank and parallel mean curvatureJournal of Differential Geometry, 39
J. Faraut, S. Kaneyuki, A. Korányi, Q. Lu, Guy Roos, C. Birkenhake, H. Lange (1999)
Analysis and Geometry on Complex Homogeneous Domains
C. Olmos (2005)
On the geometry of holonomy systems
W. Bertram (2000)
The geometry of Jordan and Lie structures, Lecture Notes in Mathematics 1754
W. Kaup (2001)
On Grassmannians associated with JB*-triplesMathematische Zeitschrift, 236
(1973)
Some extrinsic results for K¨ahler submanifolds
W. Kaup (2001)
On Grassmannians associated with $${{\rm JB}{\mathbb S}*}$$ -triplesMath. Z., 236
D. Alekseevsky, A. Scala (2004)
The Normal Holonomy Group of Kähler SubmanifoldsProceedings of the London Mathematical Society, 89
C. Olmos (1993)
Isoparametric submanifolds and their homogeneous structuresJournal of Differential Geometry, 38
A. Ros (1986)
Kaehler submanifolds in the complex projective space, Lecture Notes in Math., 1209
D. Ferus (1980)
Symmetric submanifolds of euclidean spaceMathematische Annalen, 247
J. Berndt, S. Console, C. Olmos (2003)
Submanifolds and holonomy, Research Notes in Mathematics 434
A.J. Di Scala, C. Olmos (2004)
Submanifolds with curvature normals of constant length and the Gauss mapJ. Reine Angew. Math., 574
N. Mok (1989)
Metric rigidity theorems on Hermitian locally symmetric spaces, series in pure Mathematics, vol. 6
A. Scala, Olmos Carlos (2004)
Submanifolds with curvature normals of constant length and the Gauss mapCrelle's Journal, 2004
E. Calabi, E. Vesentini (1960)
On Compact, Locally Symmetric Kahler ManifoldsAnnals of Mathematics, 71
G. Roos (2000)
Analysis and geometry on complex homogeneous domains, progress in mathematics, vol.185
(2000)
Jordan triple systems
C. Olmos (1990)
The normal holonomy group, 110
A. Ros (1985)
A Characterization of Seven Compact Kaehler Submanifolds by Holomorphic PinchingAnnals of Mathematics, 121
Thomas Cecil (1974)
Geometric applications of critical point theory to submanifolds of complex projective spaceNagoya Mathematical Journal, 55
C. Olmos (2005)
A geometric proof of the Berger Holonomy TheoremAnnals of Mathematics, 161
Console, Antonio J. Di
A. Ros (1986)
Kaehler submanifolds in the complex project space
M. Takeuchi (1978)
Homogeneous Kähler submanifolds in complex projective spacesJapanese journal of mathematics. New series, 4
Jean-Pierre Serre (1954)
Représentations linéaires et espaces homogènes kählériens des groupes de Lie compacts, 2
The object of this article is to compute the holonomy group of the normal connection of complex parallel submanifolds of the complex projective space. We also give a new proof of the classification of complex parallel submanifolds by using a normal holonomy approach. Indeed, we explain how these submanifolds can be regarded as the unique complex orbits of the (projectivized) isotropy representation of an irreducible Hermitian symmetric space. Moreover, we show how these important submanifolds are related to other areas of mathematics and theoretical physics. Finally, we state a conjecture about the normal holonomy group of a complete and full complex submanifold of the complex projective space.
Mathematische Zeitschrift – Springer Journals
Published: Jan 22, 2008
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.