On conformally Kähler, Einstein manifolds
Copyright policy )On conformally Kähler, Einstein manifolds
We prove that any compact complex surface with c 1 > 0 c_1>0 admits an Einstein metric which is conformally related to a Kähler metric. The key new ingredient is the existence of such a metric on the blow-up C P 2 # 2 C P 2 ¯ \mathbb {CP}_2\# 2\overline {\mathbb {CP}_2} of the complex projective plane at two distinct points.
- University of Wisconsin System United States
- University of Wisconsin–Oshkosh United States
- State University of New York United States
- University of Wisconsin–Madison United States
- Stony Brook University United States
Mathematics - Differential Geometry, FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), 53C25; 53C55, 53C55, General Relativity and Quantum Cosmology, 53C25, Mathematics - Algebraic Geometry, Mathematics - Analysis of PDEs, Differential Geometry (math.DG), FOS: Mathematics, Algebraic Geometry (math.AG), Analysis of PDEs (math.AP)
Mathematics - Differential Geometry, FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), 53C25; 53C55, 53C55, General Relativity and Quantum Cosmology, 53C25, Mathematics - Algebraic Geometry, Mathematics - Analysis of PDEs, Differential Geometry (math.DG), FOS: Mathematics, Algebraic Geometry (math.AG), Analysis of PDEs (math.AP)
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