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Some framed f -structures on transversally Finsler foliations

Cristian Ida — 2011

Annales UMCS, Mathematica

Some problems concerning to Liouville distribution and framed f-structures are studied on the normal bundle of the lifted Finsler foliation to its normal bundle. It is shown that the Liouville distribution of transversally Finsler foliations is an integrable one and some natural framed f(3, ε)-structures of corank 2 exist on the normal bundle of the lifted Finsler foliation.

Hodge-Bott-Chern decompositions of mixed type forms on foliated Kähler manifolds

Cristian Ida — 2014

Colloquium Mathematicae

The Bott-Chern cohomology groups and the Bott-Chern Laplacian on differential forms of mixed type on a compact foliated Kähler manifold are defined and studied. Also, a Hodge decomposition theorem of Bott-Chern type for differential forms of mixed type is proved. Finally, the case of projectivized tangent bundle of a complex Finsler manifold is discussed.

Some framed f -structures on transversally Finsler foliations

Cristian Ida — 2011

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

Some problems concerning to Liouville distribution and framed f -structures are studied on the normal bundle of the lifted Finsler foliation to its normal bundle. It is shown that the Liouville distribution of transversally Finsler foliations is an integrable one and some natural framed f ( 3 , ε ) -structures of corank 2 exist on the normal bundle of the lifted Finsler foliation.

Stability of Tangential Locally Conformal Symplectic Forms

Cristian Ida — 2014

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper we firstly define a tangential Lichnerowicz cohomology on foliated manifolds. Next, we define tangential locally conformal symplectic forms on a foliated manifold and we formulate and prove some results concerning their stability.

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