ISSN:
1434-601X
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract Starting from the infinitesimal holonomy groupH i of aV 4, (+++−) the spinholonomy group $$\tilde H_i \equiv \bar \sigma ^1 (H_i )$$ defined by the covering isomorphism $$\sigma :G \to L_ + ^ \uparrow $$ is introduced. In Einstein-spaces we may replace its real Lie-algebra by a complex one. With the complex calculus we may reproduce the results ofSchell, Goldberg andKerr with very much simplified proofs. A theorem on non-empty Einstein-spaces is given. In part 4 we prove a theorem on the connection between theH i -behaviour of a vector (spinor) and its covariant derivative in aV 4. With its help we get in a simple manner the metiics of aV 4 with givenH i and Dim (H i ) 〈6; our results agree with those given byGoldberg andKerr, Cahen andDebever. Finally we make some new statements on imperfect holonomy groups.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01381251
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