If only we could hear Norma Desmond rise up and sing: Don’t cha wish your girflriend, that little tart Betty Schaefer, was hot like me?

That does not happen in Nicole Scherzinger ‘s current run of shows, which included a diverting stop Thursday night at Walt Disney Concert Hall in downtown L.A. The show tunes stayed in their corner, and the Pussycat Dolls oldies stayed in theirs. It was a show with a slightly split personality, with musical theater numbers dominating the first three-quarters and the flashy pop perpetrated by her ex-girl-group taking over the last stretch.

But it didn’t feel like an impossibly wide chasm. Even as Scherzinger sang two bravura songs from the stage musical that brought her back into the limelight in a big way, “ Sunset Blvd. ,” you were reminded that

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