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Extremals for the Sobolev inequality on the seven-dimensional quaternionic Heisenberg group and the quaternionic contact Yamabe problem

Stefan Ivanov, Ivan Minchev, Dimiter Vassilev (2010)

Journal of the European Mathematical Society

A complete solution to the quaternionic contact Yamabe problem on the seven-dimensional sphere is given. Extremals for the Sobolev inequality on the seven-dimensional Heisenberg group are explicitly described and the best constant in the L2 Folland–Stein embedding theorem is determined.

f -biminimal maps between Riemannian manifolds

Yan Zhao, Ximin Liu (2019)

Czechoslovak Mathematical Journal

We give the definition of f -biminimal submanifolds and derive the equation for f -biminimal submanifolds. As an application, we give some examples of f -biminimal manifolds. Finally, we consider f -minimal hypersurfaces in the product space n × 𝕊 1 ( a ) and derive two rigidity theorems.

F -manifolds and integrable systems of hydrodynamic type

Paolo Lorenzoni, Marco Pedroni, Andrea Raimondo (2011)

Archivum Mathematicum

We investigate the role of Hertling-Manin condition on the structure constants of an associative commutative algebra in the theory of integrable systems of hydrodynamic type. In such a framework we introduce the notion of F -manifold with compatible connection generalizing a structure introduced by Manin.

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