What is the defining formula for sectional curvature?


$K\_1(X,Y) = \frac{ \langle R(X,Y)Y, X \rangle} {\langle X,X \rangle \langle Y,Y \rangle - \langle X,Y \rangle} $


as in <http://en.wikipedia.org/wiki/Sectional_curvature>


OR


$K\_2(X,Y) = \frac{ \langle R(X,Y)X, Y \rangle} {\langle X,X \rangle \langle Y,Y \rangle - \langle X,Y \rangle} = -K\_1(X,Y) $ since $\langle R(u,v)w,z \rangle = -\langle R(u,v)z,w \rangle$



What is the defining formula for Sectional Curvature
There is no standard sign convention for the sign curvature tensor. 
Depending on author,
the same thing is denoted as
$$\langle R(X,Y)Y, X \rangle\ \ \text{or}\ \ \langle R(X,Y)X, Y \rangle.$$ 
But the sectional curvature is always positive for sphere and always negative for Lobachevky space. That makes you to choose one of the formulas in your question.


