Previous |  Up |  Next

Article

Keywords:
locally conformal Kähler structure; minimal submanifolds; invariant submanifolds; totally real submanifolds; $CR$-submanifolds
Summary:
In this paper we obtain all invariant, anti-invariant and $CR$ submanifolds in $({\mathbb{R}}^4,g,J)$ endowed with a globally conformal Kähler structure which are minimal and tangent or normal to the Lee vector field of the g.c.K. structure.
References:
[1] D. E.  Blair, S.  Dragomir: $CR$-products in Locally Conformal Kähler Manifolds. Kyushu J.  Math. 56 (2002), 337–362. DOI 10.2206/kyushujm.56.337 | MR 1934130
[2] S.  Dragomir, L.  Ornea: Locally Conformal Kähler Geometry. Birkhäuser-Verlag, Boston-Basel-Berlin, 1998. MR 1481969
[3] S.  Dragomir: Cauchy-Riemann submanifolds of locally conformal Kaehler manifolds. Geom. Dedicata 28 (1988), 181–197. DOI 10.1007/BF00147450 | MR 0971624 | Zbl 0659.53041
[4] H.  Inage, K.  Matsumoto: $4$-dimensional Kählerian manifolds. Preprint  2004.
[5] P.  Libermann: Sur le problème d’équivalence de certaines structures infinitésimales régulières. Ann. Mat. Pura Appl. 36 (1954), 27–120. (French) DOI 10.1007/BF02412833 | MR 0066020
[6] I.  Vaisman: On locally conformal almost Kähler manifolds. Isr. J.  Math. 24 (1976), 338–351. DOI 10.1007/BF02834764 | MR 0418003 | Zbl 0335.53055
[7] K.  Yano, M.  Kon: $CR$  Submanifolds of Kaehlerian and Sasakian Manifolds. Birkhäuser-Verlag, Boston-Basel-Stuttgart, 1983. MR 0688816
Partner of
EuDML logo