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Nonsymmetric Osserman indefinite Kähler manifolds
Author(s):
A.
Bonome;
R.
Castro;
E.
García-Río;
L.
Hervella;
R.
Vázquez-Lorenzo
Journal:
Proc. Amer. Math. Soc.
126
(1998),
2763-2769.
MSC (1991):
Primary 53B30, 53C15, 53C50, 53C55
MathSciNet review:
1476121
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Abstract:
The authors prove the existence of Osserman manifolds with indefinite Kähler metric of nonnegative or nonpositive holomorphic sectional curvature which are not locally symmetric.
References:
- [1]
- M. Barros and A. Romero, Indefinite Kähler manifolds, Math. Ann. 261 (1982), 55-62. MR 84d:53033
- [2]
- N. Bla\v{z}i\'{c}, N. Bokan and P. Gilkey, A Note on Osserman Lorentzian manifolds, Bull. London Math. Soc. 29 (1997), 227-230. MR 97m:53111
- [3]
- A. Bonome, R. Castro, E. García-Río and L. Hervella, On the holomorphic sectional curvature of an indefinite Kähler manifold, C. R. Acad. Sci. Paris 315 (1992), 1183-1187. MR 93j:53079
- [4]
- A. Bonome, R. Castro, E. García-Río, L. Hervella and Y. Matsushita, Null holomorphically flat indefinite almost Hermitian manifolds, Illinois J. Math. 39 (1995), 635-660. MR 97e:53050
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- [6]
- Q.S. Chi, Curvature characterization and classification of rank-one symmetric spaces, Pacific J. Math. 150 (1991), 31-42. MR 92g:53044
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- P.M. Gadea and A. Montesinos Amilibia, Spaces of constant paraholomorphic sectional curvature, Pacific J. Math. 136 (1989), 85-101. MR 90d:53043
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- E. García-Río, D.N. Kupeli and M.E. Vázquez-Abal, On a problem of Osserman in Lorentzian geometry, Diff. Geom. Appl. 7 (1997), 85-100. CMP 97:10
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- E. García-Río, M.E. Vázquez-Abal and R. Vázquez-Lorenzo, Nonsymmetric Osserman pseudo-Riemannian manifolds, preprint.
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- P. Gilkey, A. Swann and L. Vanhecke, Isoparametric geodesic spheres and a conjecture of Osserman concerning the Jacobi operator, Quart. J. Math. Oxford 46 (1995), 299-320. MR 96h:53051
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- V. Oproiu, Harmonic maps between tangent bundles, Rend. Sem. Mat. Univ. Politecn. Torino 47 (1989), 47-55. MR 92f:58047
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- K. Yano, S. Ishihara, Tangent and cotangent bundles, Marcel Dekker, New York, 1973. MR 50:3142
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Additional Information:
A.
Bonome
Affiliation:
Facultade de Matemáticas, Universidade de Santiago de Compostela, 15706 Santiago de Compostela, Spain
R.
Castro
Affiliation:
Facultade de Matemáticas, Universidade de Santiago de Compostela, 15706 Santiago de Compostela, Spain
E.
García-Río
Affiliation:
Facultade de Matemáticas, Universidade de Santiago de Compostela, 15706 Santiago de Compostela, Spain
Email:
eduardo@zmat.usc.es
L.
Hervella
Affiliation:
Facultade de Matemáticas, Universidade de Santiago de Compostela, 15706 Santiago de Compostela, Spain
R.
Vázquez-Lorenzo
Affiliation:
Facultade de Matemáticas, Universidade de Santiago de Compostela, 15706 Santiago de Compostela, Spain
DOI:
10.1090/S0002-9939-98-04659-0
PII:
S 0002-9939(98)04659-0
Keywords:
Osserman space,
tangent bundle,
indefinite K\"{a}hler metric,
holomorphic sectional curvature,
para--K\"{a}hler metric
Received by editor(s):
January 28, 1997
Additional Notes:
Supported by projects DGICYT PB940633C0201 and XUGA 20702B96, Spain
Communicated by:
Christopher Croke
Copyright of article:
Copyright
1998,
American Mathematical Society
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