Using 2.92 fb$^{-1}$ of electron-positron annihilation data collected at a
center-of-mass energy of $sqrt{s}= 3.773$ GeV with the BESIII detector, we
present an improved measurement of the branching fraction $mathcal{B}(D^+ o
omega e^+
u_{e}) = (1.63pm0.11pm0.08) imes 10^{-3}$. The parameters
defining the corresponding hadronic form factor ratios at zero momentum
transfer are determined for the first time, we measure them to be $r_V =
1.24pm0.09pm0.06$ and $r_2 = 1.06pm0.15 pm 0.05$. The first and second
uncertainties are statistical and systematic, respectively. We also search for
the decay $D^+ o phi e^+
u_{e}$. An improved upper limit $mathcal{B}(D^+
o phi e^+
u_{e}) < 1.3 imes 10^{-5}$ is set at 90\% confidence level.
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