It can be cadence related - If turning over a big gear with low RPM's on the hill - that typically recruits more muscle fibers, but since turning over the cranks more slowly the HR goes down.
If you spin at a high cadence (90+) while climbing would see a higher HR.

Oh and ya, you are weak - now drop and give me twenty! ;)

Hi there
I am average at climbing hills, and while you don't give much detail on your build and technique, I have found the following useful:

(in no particular order)
1) anticipate the climb and get in the gear that you will need at the top early on (or even at the bottom of the climb). This way you don't lose momentum or concentration trying to find the right gear as you go up. When you select the gear for the top of the hill at the bottom of the hill it will seem too easy but stay in it and you will get up the hill effortlessly.
As you get more familiar with the climbs you will get to know what gear you can start in and maybe do one shift halfway up or at the crux.

2) Mentally welcome the hill. Don't get all down and sucky about "oh there's a hill coming up". Don't take the ride around. Ride the hill with a positive attitude.

3) You didn't say if you climb seated or standing. Climbing standing uses more energy (is less efficient) than climbing seated. Learn which hills you can power over out of the saddle (shorter climbs) and which ones you need to sit and spin your way up. You can mix it up a little to get a little momentum going but try to limit standing up.

4) Climb with your hands on the brake hoods or on the tops. Not on the drops (only Marco pantani could get away with that.)

5) When the hills seem hard, slide your butt back in the saddle a little - not too much - just an inch or so. I always feel like this gives me a better push on the pedal.

6) If the hill gets horribly steep remind yourself to pull "up" coming over the top of the stroke.

7) Change your rear cogset. If you have a 12-21 which is fairly standard on bikes and you ride hilly, look into getting a 12-26 or similar. This will ensure that you are not overgeared for the terrain.

8) Alternately, change your front inner chain ring. Bikes often ship with a 53-42 standard. Chainging the inner ring to a 39 tooth cog will give you a lower gear. Changing front and rear, from say a 42/21 t a 39/26 will help you spin more if you have been mashing the big gears up the hills.

9) Climb on heart rate. Pick a heart rate (steady etc) and ride the hill according to this or with a goal of staying within yourself.

10) Ride more hills using these techniques and (hopefully) soon you will realise that they have become easier.

Hope these help.

Maybe my question is too technical and needs to go to a sports scientist.

I am 71kg, 10% body fat, 1.79m. I would say athletic figure...

My main question is: Why can't I get my heart rate whilst riding the hills? I know if I could I'd get over them faster, every now and then I can and yep, you guessed it, I fly up.

The hills I'm on at the moment are hour climbs in The Alps, awesome but if I could work harder I wouldn't have to be out so long...........

:-)