# On compact holomorphically pseudosymmetric Kählerian manifolds

Open Mathematics (2009)

- Volume: 7, Issue: 3, page 442-451
- ISSN: 2391-5455

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topZbigniew Olszak. "On compact holomorphically pseudosymmetric Kählerian manifolds." Open Mathematics 7.3 (2009): 442-451. <http://eudml.org/doc/269598>.

@article{ZbigniewOlszak2009,

abstract = {For compact Kählerian manifolds, the holomorphic pseudosymmetry reduces to the local symmetry if additionally the scalar curvature is constant and the structure function is non-negative. Similarly, the holomorphic Ricci-pseudosymmetry reduces to the Ricci-symmetry under these additional assumptions. We construct examples of non-compact essentially holomorphically pseudosymmetric Kählerian manifolds. These examples show that the compactness assumption cannot be omitted in the above stated theorem. Recently, the first examples of compact, simply connected essentially holomorphically pseudosymmetric Kählerian manifolds are discovered in [4]. In these examples, the structure functions change their signs on the manifold.},

author = {Zbigniew Olszak},

journal = {Open Mathematics},

keywords = {Kählerian manifold; Semisymmetry; Holomorphic pseudosymmetry; Kähler manifold; holomorphic pseudosymmetry; holomorphic Ricci-pseudosymmetry; semisymmetry; Ricci-symmetry},

language = {eng},

number = {3},

pages = {442-451},

title = {On compact holomorphically pseudosymmetric Kählerian manifolds},

url = {http://eudml.org/doc/269598},

volume = {7},

year = {2009},

}

TY - JOUR

AU - Zbigniew Olszak

TI - On compact holomorphically pseudosymmetric Kählerian manifolds

JO - Open Mathematics

PY - 2009

VL - 7

IS - 3

SP - 442

EP - 451

AB - For compact Kählerian manifolds, the holomorphic pseudosymmetry reduces to the local symmetry if additionally the scalar curvature is constant and the structure function is non-negative. Similarly, the holomorphic Ricci-pseudosymmetry reduces to the Ricci-symmetry under these additional assumptions. We construct examples of non-compact essentially holomorphically pseudosymmetric Kählerian manifolds. These examples show that the compactness assumption cannot be omitted in the above stated theorem. Recently, the first examples of compact, simply connected essentially holomorphically pseudosymmetric Kählerian manifolds are discovered in [4]. In these examples, the structure functions change their signs on the manifold.

LA - eng

KW - Kählerian manifold; Semisymmetry; Holomorphic pseudosymmetry; Kähler manifold; holomorphic pseudosymmetry; holomorphic Ricci-pseudosymmetry; semisymmetry; Ricci-symmetry

UR - http://eudml.org/doc/269598

ER -

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