Geodesic
INVARIANT SUBMANIFOLDS OF CONTACT (κ, μ)-MANIFOLDS
Glasgow mathematical journal, Tome 50 (2008) no. 3, pp. 499-507

Voir la notice de l'article provenant de la source Cambridge University Press

Invariant submanifolds of contact (κ, μ)-manifolds are studied. Our main result is that any invariant submanifold of a non-Sasakian contact (κ, μ)-manifold is always totally geodesic and, conversely, every totally geodesic submanifold of a non-Sasakian contact (κ, μ)-manifold, μ ≠ 0, such that the characteristic vector field is tangent to the submanifold is invariant. Some consequences of these results are then discussed.
DOI : 10.1017/S0017089508004369
Mots-clés : Primary 53C40, Secondary 53C25, 53D10, 53D15 
MONTANO, BENIAMINO CAPPELLETTI; TERLIZZI, LUIGIA DI; TRIPATHI, MUKUT MANI. INVARIANT SUBMANIFOLDS OF CONTACT (κ, μ)-MANIFOLDS. Glasgow mathematical journal, Tome 50 (2008) no. 3, pp. 499-507. doi: 10.1017/S0017089508004369
@article{10_1017_S0017089508004369,
     author = {MONTANO, BENIAMINO CAPPELLETTI and TERLIZZI, LUIGIA DI and TRIPATHI, MUKUT MANI},
     title = {INVARIANT {SUBMANIFOLDS} {OF} {CONTACT} (\ensuremath{\kappa}, {\ensuremath{\mu})-MANIFOLDS}},
     journal = {Glasgow mathematical journal},
     pages = {499--507},
     year = {2008},
     volume = {50},
     number = {3},
     doi = {10.1017/S0017089508004369},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089508004369/}
}
TY  - JOUR
AU  - MONTANO, BENIAMINO CAPPELLETTI
AU  - TERLIZZI, LUIGIA DI
AU  - TRIPATHI, MUKUT MANI
TI  - INVARIANT SUBMANIFOLDS OF CONTACT (κ, μ)-MANIFOLDS
JO  - Glasgow mathematical journal
PY  - 2008
SP  - 499
EP  - 507
VL  - 50
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089508004369/
DO  - 10.1017/S0017089508004369
ID  - 10_1017_S0017089508004369
ER  - 
%0 Journal Article
%A MONTANO, BENIAMINO CAPPELLETTI
%A TERLIZZI, LUIGIA DI
%A TRIPATHI, MUKUT MANI
%T INVARIANT SUBMANIFOLDS OF CONTACT (κ, μ)-MANIFOLDS
%J Glasgow mathematical journal
%D 2008
%P 499-507
%V 50
%N 3
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089508004369/
%R 10.1017/S0017089508004369
%F 10_1017_S0017089508004369

[1] 1.Agut, C., Submanifolds in contact metric manifolds with a nullity condition, An. Univ. Timişoara Ser. Mat.-Inform. 41 (2003), 3–9. Google Scholar

[2] 2.Blair, D. E., Two remarks on contact metric structures, Tôhoku Math. J. 29 (1977), 319–324. Google Scholar

[3] 3.Blair, D. E., Riemannian geometry of contact and symplectic manifolds, Progress in Mathematics, 203. (Birkhäuser Boston, Inc., Boston, MA, 2002). Google Scholar

[4] 4.Blair, D. E., Koufogiorgos, T. and Papantoniou, B. J., Contact metric manifolds satisfyng a nullity condition, Israel J. Math. 91 (1995), 189–214. Google Scholar

[5] 5.Boeckx, E., A class of locally φ-symmetric contact metric spaces, Arch. Math. (Basel) 72 (1999), 466–472. Google Scholar | DOI

[6] 6.Boeckx, E., Contact-homogeneous locally φ-symmetric manifolds, Glasg. Math. J. 48 (2006), 93–109. Google Scholar

[7] 7.Boeckx, E., A full classification of contact metric (κ, μ)-spaces, Illinois J. Math. 44 (2000), 212–219. Google Scholar | DOI

[8] 8.Cappelletti, B.Montano, Bi-Legendrian connections, Ann. Polon. Math. 86 (2005), 79–95. Google Scholar

[9] 9.Cappelletti, B. Montano, Some remarks on the generalized Tanaka–Webster connection of a contact metric manifold, Rocky Mountain J. Math., to appear. Google Scholar

[10] 10.Cappelletti Montano, B. and Di Terlizzi, L., Contact metric (κ, μ)-spaces as bi-Legendrian manifolds, Bull. Austral. Math. Soc., to appear. Google Scholar

[11] 11.Chinea, D., Invariant submanifolds of a quasi-K-Sasakian manifold, Riv. Mat. Univ. Parma 11 (1985), 25–29. Google Scholar

[12] 12.Dombrowski, P., On the geometry of the tangent bundle, J. Rein Angew. Math. 210 (1962), 73–88. Google Scholar

[13] 13.Endo, H., Invariant submanifolds in a contact Riemannian manifold, Tensor 42 (1985), 86–89. Google Scholar

[14] 14.Endo, H., On the curvature tensor field of a type of contact metric manifolds and of its certain submanifolds, Publ. Math. Debrecen 48 (1996), 253–269. Google Scholar | DOI

[15] 15.Kon, M., Invariant submanifolds of normal contact metric manifolds, Kōdai Math. Sem. Rep. 27 (1973), 330–336. Google Scholar

[16] 16.Koufogiorgos, T., Contact Riemannian manifolds with constant φ-sectional curvature, Tokyo J. Math. 20 (1997), 13–22. Google Scholar

[17] 17.Kowalski, O., Curvature of the induced Riemannian metric on the tangent bundle, J. Rein Angew. Math. 250 (1971), 124–129. Google Scholar

[18] 18.Murathan, C., Arslan, K., Özgür, C. and Yildiz, A., On invariant submanifolds satisfying a nullity condition, An. Univ. Bucureşti Mat. Inform. 50 (2001), 103–113. Google Scholar

[19] 19.Sasaki, S., On the differential geometry of tangent bundle of Riemannian manifolds, Tôhoku Math. J. 10 (1958), 338–354. Google Scholar | DOI

[20] 20.Sasaki, S., On the differential manifolds with contact metric structures. Part II, Tôhoku Math. J. 14 (1962), 146–155. Google Scholar

[21] 21.Sasaki, S. and Hatakeyama, Y., On differentiable geometry of tangent bundle of Riemannian manifolds, J. Math. Soc. Japan 14 (1962), 249–271. Google Scholar

[22] 22.Tashiro, Y., On contact structures of tangent sphere bundles, Tôhoku Math. J. 21 (1969), 117–143. Google Scholar

[23] 23.Tripathi, M. M., Sasahara, T. and Kim, J.-S., On invariant submanifolds of contact metric manifolds, Tsukuba J. Math. 29 (2) (2005), 495–510. Google Scholar

[24] 24.Yano, K. and Kon, M., Structures on manifolds, Series in Pure Mathematics (World Scientific, Singapore, 1984). Google Scholar

Cité par Sources :