we study the notion of harmonicity in the sense of symplectic geometry, and investigate the geometric properties of harmonic thom forms and distributional thom currents, dual to different types of submanifolds. we show that the harmonic thom form associated to a symplectic submanifold is nowhere vanishing. we also construct symplectic smoothing operators which preserve the harmonicity of distri...

In this paper we address three problems stemming from the fundamental question: Let M be an oriented surface, how much data do we need to identify an immersion f : M → R or its shape? A generic immersion f is determined up to homothety and translation by its conformal class and its tangent plane map Tf : M → Gr(2, 3) whose value Tf (p) at each point p ∈ M is the plane tangent to the image surfa...

‎In this paper‎, ‎we‎ ‎consider‎ ‎semi‎ ‎symmetric‎ ‎submanifolds‎ ‎in‎ ‎conformal‎ ‎Kenmotsu‎ ‎manifolds‎ ‎and‎ ‎then ‎using‎ ‎obtained‎ ‎results‎ ‎for‎ ‎this‎ ‎type‎ ‎of‎ ‎submanifolds‎, ‎‎‎we‎ ‎‎‎‎characterize‎ locally symmetric submanifolds of conformal Kenmotsu ‎manifolds‎.