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We calculate the temperature $T$ and angular $(\theta,\phi)$ dependence ofthe upper critical induction $B_{c2}(\theta,\phi,T)$ for parallel-spinsuperconductors with an axially symmetric $p$-wave pairing interaction pinnedto the lattice and a dominant ellipsoidal Fermi surface (FS). For all FSanisotropies, the chiral Scharnberg-Klemm state $B_{c2}(\theta,\phi,T)$ exceedsthat of the chiral Anderson-Brinkman-Morel state, and exhibits a kink at$\theta=\theta^{*}(T,\phi)$, indicative of a first-order transition from itschiral, nodal-direction behavior to its non-chiral, antinodal-directionbehavior. Applicability to Sr$_2$RuO$_4$, UCoGe, and topologicalsuperconductors such as Cu$_x$Bi$_2$Se$_3$ is discussed.

First-order chiral to non-chiral transition in the angular dependence of the upper critical induction of the Scharnberg-Klemm $p$-wave pair state