The Bochner identities for the Kählerian gradients

Bochner-Weitzenböck formulas and curvature actions on Riemannian manifolds

Gradients are natural first order differential operators depending on Riemannian metrics. The principal symbols of them are related to the enveloping algebra and higher Casimir elements. We give certain relations in the enveloping algebra, which induce not only identities for higher Casimir elements but also all Bochner-Weitzenböck formulas for gradients. As applications, we give some vanishing...

Clifford Homomorphisms and Higher Spin Dirac Operators

We present a generalization of the Clifford action for other representations spaces of Spin(n), which is called the Clifford homomorphism. Their properties extend to the ones for the higher spin Dirac operators on spin manifolds. In particular, we have general Bochner identities for them, and an eigenvalue estimate of a Laplace type operator on any associated bundle.

The Role of Social and Place Identities towards Promoting Sustainability Approaches and Behaviors

The concept of sustainability is encouraged to preserve natural resources, social values, cultural heritage, and economic capital, which already exist to make available them for the next generations. Moreover, to enhance the level of sustainability in communities, numerous scholars indicated both individual and community identities play a crucial role. Sustainability is attainable and successfu...

Nearly Kählerian Embeddings of Symplectic Manifolds

Lp-BOUNDS FOR QUASI-GEOSTROPHIC EQUATIONS VIA FUNCTIONAL ANALYSIS

We give a proof of L-bounds for the quasi-geostrophic equation and other non-local equations. The proof uses mainly tools from functional analysis, notably the product formulas (also known as “operator splitting methods”) and the Bochner-Pollard subordination identities, hence it could be applicable to other equations. 2010 Mathematics Subject Classification: 47D06, 47F05, 35S10, 35Q99.