Conformal anti-invariant submersions from almost Hermitian manifolds

Şahin, Bayram; Akyol, Mehmet Akif

Conformal anti-invariant submersions from almost Hermitian manifolds

Mehmet Akif AKYOL, (Bingöl Üniversitesi, Fen Edebiyat Fakültesi Matematik Bölümü Bingöl Türkiye)

Bayram ŞAHİN (İnönü Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Malatya, Türkiye)

Turkish Journal of Mathematics

3 0

Yıl: 2016 Cilt: 40 Sayı: 1 Sayfa Aralığı: 43 - 70 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

Conformal anti-invariant submersions from almost Hermitian manifolds

Öz:

We introduce conformal anti-invariant submersions from almost Hermitian manifolds onto Riemannian manifolds. We give examples, investigate the geometry of foliations that arose from the definition of a conformal submersion, and find necessary and sufficient conditions for a conformal anti-invariant submersion to be totally geodesic. We also check the harmonicity of such submersions and show that the total space has certain product structures. Moreover, we obtain curvature relations between the base space and the total space, and find geometric implications of these relations.

Anahtar Kelime:

Konular: Matematik

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[1] Ali S, Fatima T. Anti-invariant Riemannian submersions from nearly Kaehler manifolds. Filomat 2013; 27: 1219 1235.
[2] Baird P, Wood JC. Harmonic Morphisms Between Riemannian Manifolds. London Mathematical Society Monographs, 29, Oxford, UK: Oxford University Press, The Clarendon Press, 2003.
[3] Bishop RL, ONeill B. Manifolds of negative curvature. Trans Amer Math Soc 1969; 145: 149.
[4] Chen BY. Riemannian submanifolds. In Dillen FJE, Verstraelen LCA, editors. Handbook of Differential Geometry, Vol. I. Amsterdam, Netherlands: North-Holland, 2000, pp. 187418.
[5] Chinea D. Harmonicity on maps between almost contact metric manifolds. Acta Math Hungar 2010; 126: 352365.
[6] Chinea D. Harmonicity of holomorphic maps between almost Hermitian manifolds. Canad Math Bull 2009; 52: 1827.
[7] Chinea D. On horizontally conformal (φ, φ´) -holomorphic submersions. Houston J Math 2008; 34: 721737.
[8] Falcitelli M, Ianus S, Pastore AM, Riemannian Submersions and Related Topics. River Edge, NJ, USA: World Scientific, 2004.
[9] Fuglede B. Harmonic morphisms between Riemannian manifolds. Ann Inst Fourier (Grenoble) 1978; 107144.
[10] Gray A. Pseudo-Riemannian almost product manifolds and submersions. J Math Mech 1967; 16: 715737.
[11] Gromoll D, Klingenberg W, Meyer W. Riemannsche Geometrie im Groβ en. Lecture Notes in Mathematics 55, Springer 1975.
[12] Gudmundsson S. The Geometry of Harmonic Morphisms. PhD Thesis, University of Leeds, Leeds, UK, 1992.
[13] Gudmundsson S, Wood JC. Harmonic morphisms between almost Hermitian manifolds. Boll Un Mat Ital B 1997; 11: 185197.
[14] G¨und¨uzalp Y., Anti-invariant semi-Riemannian submersions from almost para-Hermitian manifolds. J Funct Spaces Appl 2013, Art.ID 720623.
[15] Ishihara T. A mapping of Riemannian manifolds which preserves harmonic functions. J Math Kyoto Uni 1979; 19: 215229.
[16] Lee JW. Anti-invariant ξ ⊥ -Riemannian submersions from almost contact manifolds. Hacettepe J Math and Stat 2013; 42: 231241.
[17] Murathan C, Erken ˙IK. Anti-invariant Riemannian submersions from cosymplectic manifolds. Filomat 2015; 7: 14291444.
[18] ONeill B. The fundamental equations of a submersion. Mich Math J 1966; 13: 458469.
[19] Ponge R, Reckziegel H. Twisted products in pseudo-Riemannian geometry. Geom Dedicata 1993; 48: 1525.
[20] S¸ahin B. Anti-invariant Riemannian submersions from almost Hermitian manifolds. Central European J Math 2010; 3: 437447.
[21] Watson B. Almost Hermitian submersions. J Differential Geometry 1976; 11: 147165.
[22] Yano K, Kon M. Structures on Manifolds. Singapore: World Scientific, 1984.

APA	Akyol M, Şahin B (2016). Conformal anti-invariant submersions from almost Hermitian manifolds. , 43 - 70.
Chicago	Akyol Mehmet Akif,Şahin Bayram Conformal anti-invariant submersions from almost Hermitian manifolds. (2016): 43 - 70.
MLA	Akyol Mehmet Akif,Şahin Bayram Conformal anti-invariant submersions from almost Hermitian manifolds. , 2016, ss.43 - 70.
AMA	Akyol M,Şahin B Conformal anti-invariant submersions from almost Hermitian manifolds. . 2016; 43 - 70.
Vancouver	Akyol M,Şahin B Conformal anti-invariant submersions from almost Hermitian manifolds. . 2016; 43 - 70.
IEEE	Akyol M,Şahin B "Conformal anti-invariant submersions from almost Hermitian manifolds." , ss.43 - 70, 2016.
ISNAD	Akyol, Mehmet Akif - Şahin, Bayram. "Conformal anti-invariant submersions from almost Hermitian manifolds". (2016), 43-70.

APA	Akyol M, Şahin B (2016). Conformal anti-invariant submersions from almost Hermitian manifolds. Turkish Journal of Mathematics, 40(1), 43 - 70.
Chicago	Akyol Mehmet Akif,Şahin Bayram Conformal anti-invariant submersions from almost Hermitian manifolds. Turkish Journal of Mathematics 40, no.1 (2016): 43 - 70.
MLA	Akyol Mehmet Akif,Şahin Bayram Conformal anti-invariant submersions from almost Hermitian manifolds. Turkish Journal of Mathematics, vol.40, no.1, 2016, ss.43 - 70.
AMA	Akyol M,Şahin B Conformal anti-invariant submersions from almost Hermitian manifolds. Turkish Journal of Mathematics. 2016; 40(1): 43 - 70.
Vancouver	Akyol M,Şahin B Conformal anti-invariant submersions from almost Hermitian manifolds. Turkish Journal of Mathematics. 2016; 40(1): 43 - 70.
IEEE	Akyol M,Şahin B "Conformal anti-invariant submersions from almost Hermitian manifolds." Turkish Journal of Mathematics, 40, ss.43 - 70, 2016.
ISNAD	Akyol, Mehmet Akif - Şahin, Bayram. "Conformal anti-invariant submersions from almost Hermitian manifolds". Turkish Journal of Mathematics 40/1 (2016), 43-70.