Abstract
The mixed scalar curvature of a foliated Riemannian manifold, i.e., an averaged mixed sectional curvature, has been considered by several geometers. We explore the Yamabe type problem: to prescribe the leafwise constant mixed scalar curvature for a foliation by a conformal change of the metric in normal directions only. For a harmonic foliation, we derive the leafwise elliptic equation and explore the corresponding nonlinear heat type equation on a closed manifold (leaf). Then we assume that a foliation is defined by an orientable fiber bundle, and use spectral parameters of certain Schrödinger operator to find solution, which is an attractor of the equation.
| Original language | English |
|---|---|
| Pages (from-to) | 503-533 |
| Number of pages | 31 |
| Journal | European Journal of Mathematics |
| Volume | 1 |
| Issue number | 3 |
| DOIs | |
| State | Published - 1 Sep 2015 |
Bibliographical note
Publisher Copyright:© 2015, European Union.
Keywords
- Attractor
- Conformal
- Foliation
- Harmonic
- Leafwise Schrödinger operator
- Mixed scalar curvature
- Parabolic equation
- Riemannian metric
ASJC Scopus subject areas
- General Mathematics
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