Geodesic
On the Global Geometry of Harmonic Symmetric Bilinear Differential Forms
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 236 (2002), pp. 328-331.

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A harmonic symmetric $p$-form $\varphi$ is defined as an element of the kernel of a self-adjoint differential operator $\square$. By using the properties of this operator, the dimension of the $\mathbb R$-modulus of harmonic symmetric $p$-forms is shown to be finite on a compact Riemannian manifold. A nonexistence theorem is proved for harmonic symmetric $2$-forms tangent to the boundary of a compact Riemannian manifold. 
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M. V. Smolnikova. On the Global Geometry of Harmonic Symmetric Bilinear Differential Forms. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 236 (2002), pp. 328-331. http://geodesic.mathdoc.fr/item/TM_2002_236_a32/

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