scholarly journals THE SPECTRAL GEOMETRY OF EINSTEIN MANIFOLDS WITH BOUNDARY

2004 ◽  
Vol 41 (5) ◽  
pp. 875-882 ◽  
Author(s):  
Jeong-Hyeong Park
Keyword(s):  
Spectral Geometry ◽  
Manifolds With Boundary ◽  
Einstein Manifolds

scholarly journals An Obata-type theorem on compact Einstein manifolds with boundary

2021 ◽  
Author(s):  
Kazuo Akutagawa
Keyword(s):  
Boundary Condition ◽  
Smooth Boundary ◽  
Type Theorem ◽  
Type Inequality ◽  
Einstein Metric ◽  
Manifolds With Boundary ◽  
Einstein Manifolds ◽  
Conformal Class ◽  
Totally Geodesic ◽  
Yamabe Constant

AbstractWe show a kind of Obata-type theorem on a compact Einstein n-manifold $$(W, \bar{g})$$ ( W , g ¯ ) with smooth boundary $$\partial W$$ ∂ W . Assume that the boundary $$\partial W$$ ∂ W is minimal in $$(W, \bar{g})$$ ( W , g ¯ ) . If $$(\partial W, \bar{g}|_{\partial W})$$ ( ∂ W , g ¯ | ∂ W ) is not conformally diffeomorphic to $$(S^{n-1}, g_S)$$ ( S n - 1 , g S ) , then for any Einstein metric $$\check{g} \in [\bar{g}]$$ g ˇ ∈ [ g ¯ ] with the minimal boundary condition, we have that, up to rescaling, $$\check{g} = \bar{g}$$ g ˇ = g ¯ . Here, $$g_S$$ g S and $$[\bar{g}]$$ [ g ¯ ] denote respectively the standard round metric on the $$(n-1)$$ ( n - 1 ) -sphere $$S^{n-1}$$ S n - 1 and the conformal class of $$\bar{g}$$ g ¯ . Moreover, if we assume that $$\partial W \subset (W, \bar{g})$$ ∂ W ⊂ ( W , g ¯ ) is totally geodesic, we also show a Gursky-Han type inequality for the relative Yamabe constant of $$(W, \partial W, [\bar{g}])$$ ( W , ∂ W , [ g ¯ ] ) .

scholarly journals Geometry of compact quasi-Einstein manifolds with boundary

2021 ◽  
Author(s):  
Rafael Diógenes ◽  
Tiago Gadelha ◽  
Ernani Ribeiro
Keyword(s):  
Manifolds With Boundary ◽  
Einstein Manifolds

scholarly journals Extension of symmetries on Einstein manifolds with boundary

2010 ◽  
Vol 16 (3) ◽  
pp. 343-375 ◽  
Author(s):  
Michael T. Anderson
Keyword(s):  
Manifolds With Boundary ◽  
Einstein Manifolds
Sign in / Sign up

Export Citation Format

Share Document