Any recommendation for an internal zoom, with constant aperture across zoom , and manual iris , in the range of 35mm to 135mm and or anything in between , something that can adapt to EF mount

The Lumix 12-35 f/2.8 lives on my camera. I have tried many others including FullFrame with a SpeedBooster and by the end of day the 12-35 is back on. It is worth a lot more than your Camera and is a much better investment too.

I'm not 100% sure about vignetting with the Variogon, since I don't own a GH4. But I'm sure the corners will be very soft.

@nomad

Thanks for the feedback on the Schneider Variogon... I have a Mint Condition Tokina 28-70 Pro1 with the screw on hood that is based on the Angeniux design. The lens is actually really sharp wide open even on my full frame Nikon DSLR. However it is not parfocal, hence my interest in the Schneider Variogon. So just to confirm the Schneider will not cover the GH4 sensor in 4K mode with the extra crop? There is a guy selling a lens on Ebay and he stated in the ad that is covers the sensor in 4K mode on the GH4.

What about the Angeniux 17.5-70 do you think this would cover the GH4 in 4K mode and what are your thoughts on this lens? I would like to have at least one Parfocal lens in my quiver.

I have tons of photographic zoom lenses, and they're all parfocal. If the focus scale index lines meet the focus scale at the same place for all focal lengths, the lens is supposed to be parfocal. If the lens is even close to being parfocal, it's supposed to be parfocal. Zoom lenses are not parfocal by accident. They have an extra focus compensator group that moves with the zoom control. Varifocal lenses don't have that, and they're not even close to being parfocal - the focus shifts a lot even for small changes in the focal length. If a lens is supposed to be parfocal, it will be parfocal when the back focus is set correctly.

Here's an example of a varifocal photo lenses, the Makinon 28-80 f/3.5. Note how the focus index lines curve to match different places on the focus scale for every focal length: http://eyepatchfilms.com/?p=937

I haven't used it. I believe it's a 1" lens.

Zoom lenses are parfocal, by definition. If it's not parfocal, it's called a varifocal lens. "Varifocal zoom lens" is an oxymoron, and only a few bad lenses call themselves that.

But a zoom lens is only parfocal if its back focus is adjusted correctly. Back focus is the distance between the lens and the sensor. Inexpensive lens adapters are almost all shorter than they should be. This shifts the focus range and guarantees that you can focus to infinity (and a bit beyond), but makes zoom lenses not parfocal anymore.

More expensive adapters like the ones from Metabones and Novoflex claim to have the proper flange focal distance, but I haven't tested this myself.

I don't know of any f/2.8 zoom lenses for full frame that actually look good at f/2.8. f/3.5 is a best case scenario, and more likely f/4.0 or f/5.6. Full frame lenses are mismatched on m43 anyway, being less wide and effectively wasting the light that they collect.

The Panasonic 12-35 and 35-105 f/2.8 lenses are electronically parfocal (all Panasonic m43 zooms, actually). You lose focus while zooming, but when you stop zooming the focus motor will shift the focus back to the distance you set. So they're not great if you want to film while zooming, but they're fine if you only zoom between shots.

A C-mount lens for the 2/3" format is a pretty good match for the GH2/3/4 in 1080 ETC mode. It won't be quite as wide as on a 2/3" camera, but wider than most full frame zooms on m43. A 12.5-75 mm f/1.8 C-mount lens will be easy to find and adapt to m43 and will look good at f/2.8. Of course ETC mode comes with a noise penalty, so you'll want to keep the ISO setting as low as you can. There aren't really great options for zoom lenses and low light on the GH2. The GH4 or the a7S afford much better options. (or even a camcorder or a video-oriented superzoom like the Panasonic FZ200)

Guys, there is also another optically excellent zoom lens mentioned by Vitaliy several times:
Vivitar 28-200mm macro f/3.5-5.6
Especially for those who are on tight budget: lots of lens joy for just a little money.

I've got mine on eBay for 8€ in mint condition, FD mount. In terms of optical quality this lens meets many good primes. It is a FF lens, so it might have a great future once optical adapter / speed booster will be available.

Don't go for the 100mm f2, it is easy to brake that. The 100mm f2.5 shouldn't be too hard to find and the 135mm 2.8 is dirt cheap. An alternative to 85mm might be a Tamron SP macro 90mm 2.5, it's a very nice lens for portrait too. Slightly different color rendering to Rokkors, though.

They're not the same optical formula. Just similar specs.

I'd suspect the adapter.

I have two of the Vario Rokkors 35-70, one with and one without macro. Both great lenses and both parfocal with a Novoflex. But I've seen big differences with cheap adapters, only one out of three was about as parfocal as the Novoflex. But you can still buy 3 or 4 of them, keep the best and dump the rest – it'll still be cheaper than Novoflex. BTW, some adapters can be adjusted, the have three tiny screws which you can loosen, then there is a thread to shorten or lengthen the adapter (sorry, no brand).