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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.

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Relationship between Gaussian and bisectional curvature

Let $f:\mathbb CP^1\to X$ be an smooth embedding which its image is the curve $C$ where $X$ is a Kähler manifold. Do we have that $$\sup_{\mathbb CP^1}K(f^*\omega)<\sup_C K(\omega),$$where $K(f^*\omeg …
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