| Title:
|
Semi-slant Riemannian maps into almost Hermitian manifolds (English) |
| Author:
|
Park, Kwang-Soon |
| Author:
|
Şahin, Bayram |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
64 |
| Issue:
|
4 |
| Year:
|
2014 |
| Pages:
|
1045-1061 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We introduce semi-slant Riemannian maps from Riemannian manifolds to almost Hermitian manifolds as a generalization of semi-slant immersions, invariant Riemannian maps, anti-invariant Riemannian maps and slant Riemannian maps. We obtain characterizations, investigate the harmonicity of such maps and find necessary and sufficient conditions for semi-slant Riemannian maps to be totally geodesic. Then we relate the notion of semi-slant Riemannian maps to the notion of pseudo-horizontally weakly conformal maps, which are useful for proving various complex-analytic properties of stable harmonic maps from complex projective space and give many examples of such maps. (English) |
| Keyword:
|
Riemannian map |
| Keyword:
|
semi-slant Riemannian map |
| Keyword:
|
harmonic map |
| Keyword:
|
totally geodesic map |
| MSC:
|
53C15 |
| MSC:
|
53C42 |
| MSC:
|
53C43 |
| idZBL:
|
Zbl 06433713 |
| idMR:
|
MR3304797 |
| DOI:
|
10.1007/s10587-014-0152-3 |
| . |
| Date available:
|
2015-02-09T17:40:58Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144160 |
| . |
| Reference:
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[1] Abraham, R., Marsden, J. E., Ratiu, T.: Manifolds, Tensor Analysis, and Applications (2nd edition).Applied Mathematical Sciences 75 Springer, New York (1988). MR 0960687, 10.1007/978-1-4612-1029-0 |
| Reference:
|
[2] Aprodu, M. A., Aprodu, M.: Implicitly defined harmonic PHH submersions.Manuscr. Math. 100 (1999), 103-121. Zbl 0938.53035, MR 1714452, 10.1007/s002290050198 |
| Reference:
|
[3] Aprodu, M. A., Aprodu, M., Brînzănescu, V.: A class of harmonic submersions and minimal submanifolds.Int. J. Math. 11 (2000), 1177-1191. Zbl 0978.58006, MR 1809307, 10.1142/S0129167X0000057X |
| Reference:
|
[4] Baird, P., Wood, J. C.: Harmonic Morphisms Between Riemannian Manifolds.London Mathematical Society Monographs. New Series 29 Clarendon Press, Oxford University Press, Oxford (2003). Zbl 1055.53049, MR 2044031 |
| Reference:
|
[5] Bejancu, A.: Geometry of CR-Submanifolds.Mathematics and Its Applications (East European Series) 23 D. Reidel Publishing Co., Dordrecht (1986). Zbl 0605.53001, MR 0861408 |
| Reference:
|
[6] Burns, D., Burstall, F., Bartolomeis, P. de, Rawnsley, J.: Stability of harmonic maps of Kähler manifolds.J. Differ. Geom. 30 (1989), 579-594. Zbl 0678.53062, MR 1010173, 10.4310/jdg/1214443603 |
| Reference:
|
[7] Candelas, P., Horowitz, G. T., Strominger, A., Witten, E.: Vacuum configurations for superstrings.Nuclear Phys. B (electronic only) 258 (1985), 46-74. MR 0800347 |
| Reference:
|
[8] Chen, B.-Y.: Geometry of Slant Submanifolds.Katholieke Universiteit Leuven, Dept. of Mathematics, Leuven (1990). Zbl 0716.53006, MR 1099374 |
| Reference:
|
[9] Chen, B.-Y.: Slant immersions.Bull. Aust. Math. Soc. 41 (1990), 135-147. Zbl 0677.53060, MR 1043974, 10.1017/S0004972700017925 |
| Reference:
|
[10] Chinea, D.: Almost contact metric submersions.Rend. Circ. Mat. Palermo (2) 34 (1985), 89-104. Zbl 0589.53041, MR 0790818, 10.1007/BF02844887 |
| Reference:
|
[11] Eells, J. J., Sampson, J. H.: Harmonic mappings of Riemannian manifolds.Am. J. Math. 86 (1964), 109-160. Zbl 0122.40102, MR 0164306, 10.2307/2373037 |
| Reference:
|
[12] Esposito, G.: From spinor geometry to complex general relativity.Int. J. Geom. Methods Mod. Phys. 2 (2005), 675-731. Zbl 1086.83025, MR 2162076, 10.1142/S0219887805000752 |
| Reference:
|
[13] Falcitelli, M., Ianus, S., Pastore, A. M.: Riemannian Submersions and Related Topics.World Scientific, River Edge, New York (2004). Zbl 1067.53016, MR 2110043 |
| Reference:
|
[14] Fischer, A. E.: Riemannian maps between Riemannian manifolds.Mathematical aspects of classical field theory. Proc. of the AMS-IMS-SIAM Joint Summer Research Conf., Seattle, Washington, USA, 1991 Contemp. Math. 132 American Mathematical Society, Providence (1992), 331-366 M. J. Gotay et al. Zbl 0780.53033, MR 1188447, 10.1090/conm/132/1188447 |
| Reference:
|
[15] García-Río, E., Kupeli, D. N.: Semi-Riemannian Maps and Their Applications.Mathematics and Its Applications 475 Kluwer Academic Publishers, Dordrecht (1999). Zbl 0924.53003, MR 1700746 |
| Reference:
|
[16] Gray, A.: Pseudo-Riemannian almost product manifolds and submersions.J. Math. Mech. 16 (1967), 715-737. Zbl 0147.21201, MR 0205184 |
| Reference:
|
[17] Ianuş, S., Mazzocco, R., Vîlcu, G. E.: Riemannian submersions from quaternionic manifolds.Acta Appl. Math. 104 (2008), 83-89. Zbl 1151.53329, MR 2434668, 10.1007/s10440-008-9241-3 |
| Reference:
|
[18] Lerner, D. E., eds., P. D. Sommers: Complex Manifold Techniques in Theoretical Physics.Research Notes in Mathematics 32 Pitman Advanced Publishing Program San Francisco (1979). Zbl 0407.00015, MR 0564439 |
| Reference:
|
[19] Loubeau, E., Slobodeanu, R.: Eigenvalues of harmonic almost submersions.Geom. Dedicata 145 (2010), 103-126. Zbl 1194.53055, MR 2600948, 10.1007/s10711-009-9409-7 |
| Reference:
|
[20] Marrero, J. C., Rocha, J.: Locally conformal Kähler submersions.Geom. Dedicata 52 (1994), 271-289. Zbl 0810.53054, MR 1299880, 10.1007/BF01278477 |
| Reference:
|
[21] O'Neill, B.: The fundamental equations of a submersion.Mich. Math. J. 13 (1966), 459-469. Zbl 0145.18602, MR 0200865, 10.1307/mmj/1028999604 |
| Reference:
|
[22] Papaghiuc, N.: Semi-slant submanifolds of a Kaehlerian manifold.An. Ştiinţ. Univ. Al. I. Cuza Iaşi, Ser. Nouă, Mat. 40 (1994), 55-61. Zbl 0847.53012, MR 1328947 |
| Reference:
|
[23] Şahin, B.: Slant Riemannian maps to Kähler manifolds.Int. J. Geom. Methods Mod. Phys. 10 (2013), Paper No. 1250080, 12 pages. Zbl 1263.53025, MR 3004125, 10.1142/S0219887812500806 |
| Reference:
|
[24] Şahin, B.: Semi-invariant Riemannian maps to Kähler manifolds.Int. J. Geom. Methods Mod. Phys. 8 (2011), 1439-1454. Zbl 1242.53039, MR 2873816, 10.1142/S0219887811005725 |
| Reference:
|
[25] Şahin, B.: Invariant and anti-invariant Riemannian maps to Kähler manifolds.Int. J. Geom. Methods Mod. Phys. 7 (2010), 337-355. Zbl 1193.53148, MR 2646767, 10.1142/S0219887810004324 |
| Reference:
|
[26] Tromba, A. J.: Teichmüller Theory in Riemannian Geometry: Based on Lecture Notes by Jochen Denzler.Lectures in Mathematics ETH Zürich Birkhäuser, Basel (1992). Zbl 0785.53001, MR 1164870 |
| Reference:
|
[27] Watson, B.: Almost Hermitian submersions.J. Differ. Geom. 11 (1976), 147-165. Zbl 0355.53037, MR 0407784, 10.4310/jdg/1214433303 |
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