A note on the basic Lichnerowicz cohomology of transversally Kählerian foliations

Mathematics – Differential Geometry

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Scientific paper

In this paper we study basic Lichnerowicz cohomology of K\"{a}hlerian foliations. An $(0,2)$-basic Euler class and an associated Gysin sequence of K\"{a}hlerian flows are investigated. Also, a basic Lichnerowicz cohomology of transversally locally conformally K\"{a}hlerian foliations is studied as well as its relation with basic Bott-Chern cohomology and basic holomorphic cohomology of a foliated complex line bundle.

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