Analog of selfduality in dimension nine
Analog of selfduality in dimension nine
Abstract We introduce a type of Riemannian geometry in nine dimensions, which can be viewed as the counterpart of selfduality in four dimensions. This geometry is related to a 9-dimensional irreducible representation of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>S</m:mi> <m:mi>O</m:mi> <m:mo>(</m:mo> <m:mn>3</m:mn> <m:mo>)</m:mo> <m:mo>×</m:mo> <m:mi>S</m:mi> <m:mi>O</m:mi> <m:mo>(</m:mo> <m:mn>3</m:mn> <m:mo>)</m:mo> </m:mrow> </m:math> $\textup …