Differential operators on almost-Hermitian manifolds and harmonic forms
Nicoletta Tardini, Адриано Томассини
Abstract
We consider several differential operators on compact almost-complex, almost-Hermitian and almost-Kähler manifolds. We discuss Hodge Theory for these operators and a possible cohomological interpretation. We compare the associated spaces of harmonic forms and cohomologies with the classical de Rham, Dolbeault, Bott-Chern and Aeppli cohomologies.
Topics & Concepts
Hermitian matrixMathematicsPure mathematicsHodge theoryHarmonicHermitian manifoldInterpretation (philosophy)Differential formDifferential (mechanical device)Operator theoryDifferential operatorDifferential geometryPhysicsLinguisticsGeometryQuantum mechanicsRicci curvatureCohomologyThermodynamicsPhilosophyCurvatureGeometry and complex manifoldsAlgebraic Geometry and Number TheoryAdvanced Algebra and Geometry