caa a22 4500 445884428 CHVBK 20180317145554.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s10711-010-9503-x doi (NATIONALLICENCE)springer-10.1007/s10711-010-9503-x Gomez Ralph Department of Mathematics and Statistics, Swarthmore College, 19081, Swarthmore, PA, USA aut Lorentzian Sasaki-Einstein metrics on connected sums of S 2 × S 3 [Elektronische Daten] [Ralph Gomez] We settle completely an open problem formulated by Boyer and Galicki in [5] which asks whether or not #kS 2 × S 3 are negative Sasakian manifolds for all k. As a consequence of the affirmative answer to this problem, there exists so-called Sasaki η-Einstein and Lorentzian Sasaki-Einstein metrics on these five-manifolds for all k and moreover all of these can be realized as links of isolated hypersurface singularities defined by weighted homogenous polynomials. The key step is to construct infinitely many hypersurfaces in weighted projective space that contain branch divisors $${\Delta=\sum_{i}\left(1-\frac{1}{m_{i}}\right)D_i}$$ such that the D i are rational curves. Springer Science+Business Media B.V., 2010 Lorentzian Sasaki-Einstein nationallicence Orbifold nationallicence Branch divisor nationallicence Geometriae Dedicata Springer Netherlands 150/1(2011-02-01), 249-255 0046-5755 150:1<249 2011 150 10711 https://doi.org/10.1007/s10711-010-9503-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10711-010-9503-x text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Gomez Ralph Department of Mathematics and Statistics, Swarthmore College, 19081, Swarthmore, PA, USA aut NATIONALLICENCE 773 0- Geometriae Dedicata Springer Netherlands 150/1(2011-02-01), 249-255 0046-5755 150:1<249 2011 150 10711 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer