Clairaut and Einstein conditions for locally conformal Kaehler submersions

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Pirinççi B., Çimen Ç., Ulusoy D.

Istanbul Journal of Mathematics, cilt.1, sa.1, ss.28-39, 2023 (Hakemli Dergi)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 1 Sayı: 1
• Basım Tarihi: 2023
• Doi Numarası: 10.26650/ijmath.2023.00003
• Dergi Adı: Istanbul Journal of Mathematics
• Sayfa Sayıları: ss.28-39
• İstanbul Üniversitesi Adresli: Evet

Özet

In the present paper, we study Clairaut submersions and Einstein conditions whose total manifolds are locally conformal Kaehler manifolds. We first give a necessary and sufficient condition for a curve to be geodesic on total manifold of a locally conformal Kaehler submersion. Then, we investigate conditions for a locally conformal Kaehler submersion to be a Clairaut submersion.We find the Ricci and scalar curvature formulas between any fiber of the total manifold and the base manifold of a locally conformal Kaehler submersion and give necessary and sufficient conditions for the total manifold of a locally conformal Kaehler submersion to be Einstein. Finally, we obtain some formulas for sectional and holomorphic sectional curvatures for a locally conformal Kaehler submersion.