Invariant <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>f</mml:mi></mml:math>-structures on the flag  manifolds
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mtext>SO</mml:mtext><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:mtext>SO</mml:mtext><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>×</mml:mo><mml:mtext>SO</mml:mtext><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:mn>3</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>

Balashchenko, Vitaly V.; Sakovich, Anna

doi:https://doi.org/10.1155/IJMMS/2006/89545

International Journal of Mathematics and Mathematical Sciences

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Volume 2006 | Article ID 089545 | https://doi.org/10.1155/IJMMS/2006/89545

Invariant f-structures on the flag manifolds SO(n)/SO(2)×SO(n−3)

Vitaly V. Balashchenko¹and Anna Sakovich¹

Received17 Jul 2005

Revised19 Dec 2005

Accepted04 Jan 2006

Published12 Apr 2006

Abstract

We consider manifolds of oriented flags SO(n)/SO(2)×SO(n−3)(n≥4) as 4- and 6-symmetric spaces and indicate characteristic conditions for invariant Riemannian metrics under which the canonical f-structures on these homogeneous Φ-spaces belong to the classes Kill f, NKf, and G1f of generalized Hermitian geometry.

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Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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