Surveys in Mathematics and its Applications

ISSN 1842-6298
 Volume 1 (2006), 99 - 109

NORMAL ANTI-INVARIANT SUBMANIFOLDS OF PARAQUATERNIONIC KÄHLER MANIFOLDS

Novac-Claudiu Chiriac

Abstract. We introduce normal anti-invariant submanifolds of paraquaternionic Kähler manifolds and study the geometric structures induced on them. We obtain necessary and sufficient conditions for the integrability of the distributions defined on a normal anti-invariant submanifold. Also, we present characterizations of local (global) anti-invariant products.

2000 Mathematics Subject Classification: 53C26, 53C12, 51H25.
Keywords: paraquaternionic Kähler manifolds, foliations, totally geodesic.

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References

  1. A. Bejancu, Geometry of CR-Submanifolds, D. Reidel Publish. Comp., Dordrecht, 1986. MR0861408(87k:53126). Zbl 0605.53001.

  2. A. Bejancu and H.R. Farran, Foliations and Geometric Structures, Springer, Berlin, 2006. MR2190039(2006j:53034). Zbl 1092.53021.

  3. B.Y. Chen, Geometry of Submanifolds, Marcel Dekker, New York, 1973. MR0353212(50 #5697). Zbl 0262.53036.

  4. E. Garcia-Rio, Y. Matsushita and R. Vazquez-Lorenzo, Paraquaternionic Kähler Manifolds, Rocky Mountain J. Math., 31 (2001), 237-260. MR1821379(2001k:53088). Zbl 0987.53020.

  5. B.L. Reinhart, Foliated manifolds with bundle--like metrics, Annals Math., 69 (2) (1959), 119--132. MR0107279(21 #6004). Zbl 0122.16604.

  6. B.L. Reinhart, Differential Geometry of Foliations, Springer--Verlag, Berlin, 1983. MR2190039(2006j:53034). Zbl 0506.53018.

  7. Ph. Tondeur, Geometry of Foliations, Monographs in Mathematics. 90 Basel: Birkhäuser, Basel, 1997. MR1456994(98d:53037). Zbl 0905.53002.

  8. H. Wu, On the de Rham Decomposition Theorem, Illinois J. Math., 8 (1964), 291-311. MR0161280(28 #4488). Zbl 0122.40005.

Acknowledgement. This work was supported by the CEEX grant ET65/2005, contract no 2987/11.10.2005, from the Romanian Ministry of Education and Research.

Novac-Claudiu Chiriac
University Constantin Brâncuşi of Târgu-Jiu,
Bld. Republicii 1, 210152, Târgu-Jiu,
Romania.
e-mail: novac@utgjiu.ro
http://www.utgjiu.ro/math/nchiriac/

http://www.utgjiu.ro/math/sma