Abstract：Let $X$ be a compact connected smooth manifold with boundary. The paper deals with contact $1$-forms $\beta$ on $X$, whose Reeb vector fields $v_\b$ admit Lyapunov functions $f$. We prove that any odd-dimensional $X$ admits such a contact form.We tackle the question: how to recover $X$ and $\beta$ from the appropriate data along the boundary $\partial X$? We describe such boundary dat...
AbstractThe first non-round Einstein metrics on spheres were described in 1973 by Jensen in dimensions 4n+3 (n >0). For the next 25 years it remained an open problem whether the same could be done in even dimensions. This question was settled in 1998 when C. Böhm constructed infinite families of Einstein metrics on all Spheres of dimension between 5 and 9, in particular on $S^6$ and $S^8$. Over...
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